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COPYRIGHT DEPOSnv 



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A Comparative Study of Achievement 
in Country and Town Schools 

By Norman Frost, Ph.D. 



TEACHERS COLLEGE, COLUMBIA UNIVERSITY 
CONTRIBUTIONS TO EDUCATION, NO. Ill 



Published by 

"Vmthtrs (Snllsg?, dnlutnbta Ulmtisrattg 

New York City 

1921 



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■'•aofr 



Copyright, 1921, by Norman Frost 



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(^ilG i5 1921 m'quiddy printing CO. 

NASHVILLE 



g)ClA6305<J7 



ACKNOWLEDGMENTS 

THIS study has been made possible by the help of a number of peo- 
ple. Thanks are extended to the school officials who have fur- 
nished data or permitted tests to be given in the schools in their charge. 
Indebtedness is acknowledged to the many members of the faculty of 
Teachers College, Columbia University, who have assisted by con- 
structive criticism. Special thanks are due Dr. N. L. Engelhardt, Dr. 
G. D. Strayer and Dr. E. L. Thorndike for advice, suggestion and 
encouragement. 

N. F. 



CONTENTS 

I. Previous Objective Studies of Achievement in Country 

Schools 7 

II, Purpose and Scope of the Present Study 15 

III. Achievement Measured by the Trabue Language Scales . 18 

IV. Achievement Measured by the Courtis Standard Research 

Tests in Arithmetic Series B 33 

V. Achievement Measured by the Thomdike Silent Reading 

Scale Alpha 2 56 

VI. Summary and Conclusions 61 

Appendix 68 



A COMPARATIVE STUDY OF ACHIEVEMENT 
IN COUNTRY AND TOWN SCHOOLS 

CHAPTER I 

PREVIOUS OBJECTIVE STUDIES OF ACHIEVEMENT IN 
COUNTRY SCHOOLS 

An accurate comparison of school systems in objective terms is 
necessary for the proper solution of problems in regard to the organi- 
zation and administration of schools. Such a comparison is made 
possible by the use of standardized tests in the systems to be compared, 
and has been made with great profit in many city school systems. To 
a much more limited extent the same kind of comparisons have been 
made among rural schools. 

The Ohio Survey Commission Report, 1914, on pages 133 and 134, 
reports the median score on the Hillegas scale of 97 eighth grade 
composition papers from Delaware (city) as 521.6, and the sim- 
ilar median of 118 eighth grade composition papers from Dela- 
ware (county) is reported as 387.6. On pages 135j^. of the same 
report results of handwriting scores by the Ayres Scale are given. 
These results are from 1,397 pupils in 176 rural schools in 21 coun- 
ties in Ohio ; from 214 pupils in the three upper grades of the rural 
schools of Delaware County ; from 312 pupils in the three upper grades 
in the city schools of Delaware ; and from a small city in Iowa, based on 
results obtained by I. King and H. Johnson, whose study was originally 
published in the Journal of Educational Psychology (III: 514-520). 
Tables are given which show, among other things, that in the small 
Iowa city 98 per cent of the eighth grade papers were scored over 50 
on the Ayres Scale ; that 77.8 per cent of the like papers from the Ohio 
rural schools made like scores ; 73.5 per cent from the Delaware County 
(rural) ; and 91.3 per cent from the city of Delaware. In conclusion 
it is stated that "the handwriting in both Delaware city and Iowa city 
is on the whole better than in the rural schools . . ." and that 
"there is greater uniformity in the city schools." 

Results of work with the Courtis Standard Research Tests in 
Arithmetic Series B and Starch's Arithmetical Scale A are reported 
on pages 33j^. of A Study of Rural Schools in Travis County, Bul- 
letin of the University of Texas, December, 1916. Tables are given 
showing grade results of the Courtis tests, and the discussion is sum- 

7 



8 Study of Achievement in Country and Town Schools 

marized in this statement : "In every instance the number of examples 
attempted and the number of examples worked correctly were lower 
in this group of country schools than for the corresponding grades in 
Boston and Detroit, and among the 11,800 pupils tested in Iowa. 
Sometimes this difference was as great as 50 per cent, the average dif- 
ference being approximately 25.5 per cent." Concerning the results of 
the Starch test the following statement is made: "As a test for the 
reasoning ability of these pupils on arithmetical problems, Starch's 
Arithmetical Scale A was used. The results from the fourth to the 
eighth grade were duly tabulated. Each grade scored below the scale 
standard established for it. The fourth grade was 11 per cent below 
standard; the fifth grade 19 per cent; the sixth grade 5 per cent; the 
seventh grade 6 per cent ; and the eighth grade 8 per cent." 

In 1916 the State Board of Education in Connecticut made a num- 
ber of studies of the schools in certain of the towns (townships) of 
that state. The tests used were not standardized, but they were uni- 
form for all of these investigations. The subjects covered were arith- 
metic, reading, language, history, geography and spelling. Compara- 
tive tables for different towns in the state are given in these reports, 
which were published separately as bulletins of the Connecticut State 
Board of Education. The following quotations give an idea of the 
character of the findings : "The accomplishment of the pupils as shown 
by the tests given is only from fair to poor. Especially is this true 
in view of the retardation in the schools." {Educational Enquiry, 
Trumbull, p. 29.) "While the results in this fundamental test are not 
satisfactory, they nevertheless compare favorably with the work of 
pupils in the towns of Seymour, Westbrook and Bloomfield." {Edu- 
cational Enquiry, New Hartford, p. 24.) "It would appear from the 
above that the children cannot add with facility and accuracy, although 
some progress is being made from grade to grade." {Educational 
Enquiry, Seymour, p. 23.) "It is obvious that most pupils in these 
towns are unable to interpret and solve correctly simple problems." 
{Educational Enquiry, Westbrook, p. 25.) 

In an unpublished survey of the Haldane school. Cold Springs, N. Y., 
made in 1917, a table on page 30 gives a comparison of median achieve- 
ments in English composition by grades (Hillegas Scale, Nassau 
County Extension), which includes grade medians for the schools of 
Mobile County, Ala., and for the city of Mobile. In every grade re- 
ported the median for the city schools is higher than that for the 
country schools. 



Previous Objective Studies 9 

The Survey and Report of The Virginia Public Schools Education 
Commission, published in 1919, gives comparative results for country 
and city schools for the following tests : Thorndike Reading Scale A2, 
Virginia Reading Test Sigma 8, Virginia General Examination Exer- 
cise 1, Ay res Spelling Scale, Starch Scale for Measuring Handwriting, 
Woody Arithmetic Scale Series B, Courtis Standard Research Test 
in Arithmetic Series B, and the Nassau County Supplement to the 
Hillegas Scale for Measuring English Composition. About sixteen 
thousand different children were examined with from six to forty dif- 
ferent tests. Of these sixteen thousand children about five thousand 
were in grades three to seven of rural white schools. The general 
character of the results is indicated by the following quotations from 
the report : "In summary it may be said that the condition of reading 
in the Virginia city schools is fairly satisfactory. Such deficiencies 
as do exist will be easily adjusted when once attention is called to them. 
In the rural schools, however, there is a deficiency that should be met 
by vigorous remedial measures." (p. 121.) In regard to handwriting 
the report has this to say: "The scores for rural schools having four 
or more rooms compare favorably with those for city schools, and the 
progress is regular from grade to grade. The average progress is 
four-tenths of a scale step per year, which is less than it should be by 
Starch Standards. The one-room country school shows the poorest 
record." (p. 122.) In regard to spelling it says: "The most notable 
deficiencies are in the one-room school (all grades) and in the seventh 
grade for every group tested. In three cases the deficiency is a year 
or more of progress as measured on the Ayres Scale." (p. 123.) 
Concerning arithmetic the report states that "The average seventh 
grade score for Virginia city children at the end of the year is 15.9, 
which is the sixth grade Woody Standard for the beginning of the 
year, and it is 15.1, or less than the sixth grade Woody Standard for 
the seventh grade in the best graded rural schools. For the one-room 
rural schools it is only 13.5." (p. 124.) "What is true of addition 
is generally true of the results in subtraction, multiplication and divi- 
sion." (p. 125.) In general conclusion in regard to the results in 
rural schools the report says : "The inferiority of the small rural school 
is apparent from the figures given. In reality that inferiority is even 
greater since in all non-city schools children are on the average about 
a year older than city children and in the one-room schools children 
are on the average about a year and a half older than city children in 
each of the upper grades of the elementary schools. In arithmetic the 



10 Study of Achievement in Country and Town Schools 

inferiority of the one-room school is perhaps most marked, children 
in such schools being on the average one grade behind children in the 
larger non-city schools." (p. 129.) 

E. H. Taylor, in an article, "A Comparison of the Arithmetical 
Abilities of Rural and City School Children," published in the Journal 
of Educational Psychology (V: 461-466, October, 1914), reports the 
results of Courtis arithmetic tests given by himself and the county 
superintendent to most of the children in a county in Illinois. Tests 
were given to 309 children in 28 schools. Results are tabulated and 
compared by grades with scores of 7,008 children, published by Courtis 
in Elementary School Teacher (XII: 133/). The comparison shows 
that the rural schools are consistently below the others ; grades 3 and 
4 of the rural schools are approximately a grade below, grades 5 and 6 
are almost two grades below, grade 7 is more than one grade but less 
than two grades below, and grade 8 is at least two grades below. 

Richard Zeidler reports in Elementary School Journal (XVI : 542- 
555) tests of efficiency in the rural and village schools of Santa 
Clara County, CaHfornia. Courtis arithmetic tests were given by the 
writer to 587 children in grades 5 to 8 inclusive. Results are compared 
with a group of 20 small Western cities, with Salt Lake City, and with 
Butte. The writer concludes that "From these tables it will be noted 
that rural and village schools in Santa Clara County, in every subject 
and in every grade, fall below the median scores for the cities. This 
inferiority ranges as high as 600 per cent, as is shown in division in 
the fifth grade of Santa Clara County compared with the fifth grade 
division in Salt Lake City, Utah. It must be admitted, however, that 
Salt Lake City has an enviable record." ". . . It will be seen that 
rural and village schools of Santa Clara County fall, on the average, 
fully two grades below Salt Lake City, and one grade below the twenty 
small cities." 

The same author reports tests in silent reading in the rural 
schools of Santa Clara County, California, in Elementary School 
Journal (XVII: 55-62). Starch Reading Tests were given by the 
writer in 26 rural schools. Eight of these schools were one-teacher 
schools, 7 were two-teacher, 7 were three-teacher, and 4 had more 
than three teachers. The results are tabulated in detail, and compared 
with results from San Jose. Mr. Zeidler says : "In comparing the 
median number of words read per second in the rural schools with 
the medians for the San Jose schools, it will be seen that the rural 
schools compare very favorably with the city schools. The fifth grade 



Previous Objective Studies 11 

falls 2/10 below, while the seventh and eighth grades score higher 
than the city schools of that community. But if we make a compari- 
son of both the rural schools of Santa Clara County and the city 
schools of San Jose with the standardized scores, we find that both fall 
below, with the single exception of the seventh grade in the rural 
schools, which surpasses the standards by 1/10." "In the reproduction 
of the thought, the rural school children fall below the children of the 
city of San Jose. There is a marked difference in the third grade, 
where the median for the rural schools is 7.5 as against 12.5 in the 
city." 

Charles L. Harlan is the author of "A Comparison of the Writing, 
Spelling and Arithmetic Abilities of Country and City Children," pub- 
lished in Educational Administration and Supervision (II: 560-573). 
Tests were given to 359 pupils in 21 rural schools in a "typical" county 
in Pennsylvania. Handwriting was scored on the Ayres Scale and 
compared with Freeman's average based on a study of handwriting 
in 56 cities. No material difference appears between the results in 
Mr. Harlan's study and the averages obtained by Freeman, either in 
the quality or the speed of writing. Three hundred and thirty-seven 
pupils were tested in spelling, words being used from the Ayres list. 
Results are tabulated, and Mr. Harlan concludes : "A comparison of 
the above averages shows an advantage of from seven to fourteen 
words per one hundred in favor of the city pupils. The country 
averages are uniformly lower than the city averages. This is no mere 
statistical accident. The pupils of the rural schools do not spell as 
well on written tests as do the children of the city schools." Courtis 
Arithmetic Tests Series B were given to 255 pupils. The comparison 
is with the Courtis Standards. "In summarizing, one may say that in 
the fundamental operations of arithmetic the pupils of the rural 
schools rank approximately two grades below the pupils of the city 
schools." "The improvement in arithmetic from grade to grade is 
less for country children than for city children." 

M. E. Haggerty, in Studies in Arithmetic, Indiana University 
Studies, No. 32 (September, 1916), reports results from 5 counties 
in Indiana. Results are tabulated, and it is concluded that "These 
data point to the conclusion that the district schools are more efficient 
in procuring achievement in the function measured than the graded." 
(p. 68.) This is the only study found that reports an actual advan- 
tage in favor of the rural school. Mr. Paul Mort is directly responsi- 
ble for the data collected. It is not definitely stated how the material 



12 Study of Achievement in Country and Tozvn Schools 

given in this study was gathered, but it is to be inferred from the ex- 
tent of the study that the testing was done by the teachers. 

In A Report on the Use of Some Standard Tests, Wisconsin State 
Department of Public Instruction Studies in Educational Measure- 
ments in Wisconsin, Bulletin No. 1, W. W. Theisen reports results 
for 36,564 children in Wisconsin, of whom 15,825 were in rural schools. 
He summarizes on page 22 as follows : ''Judged by the Ayres stand- 
ards, rural children in Wisconsin do not spell well. They average not 
less than 10 points below the standard in every grade. However, 
when compared with other classes of Wisconsin schools, as will be 
seen from Table 1, they are not conspicuously poorer nor better spell- 
ers than the pupils in the cities and villages." 

The same author in the same report gives results of penmanship 
scored according to the Thorndike Handwriting Scale from 141 rural 
schools in 28 counties. He summarizes (p. 85) : "Rural schools on the 
whole make the best showing of Wisconsin schools in writing. Their 
quality is not inferior to that of other classes of schools, and their 
speed is more nearly in accord with desirable standards in most grades." 

The Sixty-Ninth Report of the Public Schools of the State of Mis- 
souri (June 30, 1918) reports a series of investigations as to rural 
school conditions in that state. Courtis Standard Reading Test No. 2 
was given to 6,056 pupils in 547 schools in 82 counties. Among the 
findings it is stated (p. 74) that "A second observation based on the 
table is that in all three phases of reading ability the rural school chil- 
dren in these grades (2-8) are below the standard set by Courtis." 

The Kansas City Scale for Measuring Handwriting was used for 
scoring papers of about 8,000 pupils in 86 counties in the same state. 
The results are reported in detail by grades, and it is concluded (pp. 
80-81) that "The quality or form of handwriting of the rural school 
pupils is far below the accepted standards, grade for grade. The 
speed is above the accepted standards, except in the seventh and eighth 
grades." 

Results are also reported from 6,445 pupils in grades 4 to 8 inclu- 
sive and from 87 counties for the use of Courtis Standard Research 
Tests in Arithmetic, Series B. (pp. 81-85.) It is concluded that 
"On the whole the rural school children in Missouri are not up to the 
ability of the city pupils as shown by the Courtis general tabulations. 
This is particularly true of the sixth, seventh and eighth grades. In 
the eighth grade it was pointed out that the Missouri rural school pu- 
pils were below in every particular." 



Previous Objective Studies 13 

In the same report (pp. 85-87) results are given for a spelling test 
based on the Ayres' Spelling Scale given to 8,326 pupils in 611 schools 
in 86 counties. In conclusion it is stated (p. 87) that "The rural 
school pupils in Missouri are below the standard attainment for the 
city school pupils in 84 of the larger cities of the United States, and 
the writer of the report of which this section is a summary says also 
that the rural school pupils are below the attainment of the ten town 
schools in the state studied by him." 

In 1918, in Report on Spelling and Penmanship in Country Schools, 
Louisiana State Department of Education, Bulletin No. 1, June, 
1918, John M. Foote reported the results of spelling test from the Ayres 
list given to 4,584 pupils in rural schools in Louisiana. He concludes 
(p. 11) that : "While it may be that the superiority of the large type of 
school as compared with the small type is decisively reflected in the 
instruction in some of the subjects taught, it must be concluded that 
in so far as spelling ability in the rural schools is concerned no such 
decisive difference exists. The results show clearly that there is a 
difference in favor of the large school, but the assumption that the 
classroom results are very much better is not warranted." 

The same author in the same bulletin reports handwriting results 
according to the Ayres Scale for 4,073 pupils in 114 rural schools, 
and concludes (p. 24) that "It will be seen by reference to the table 
and diagram that there is comparatively little difference in both qual- 
ity and speed between the five groups. It will be noted that the dif- 
ference in quality is less than in speed. The situation is similar to that 
found in spelling. The evidence therefore points to the conclusion 
that the pupils in the large schools are slightly superior, but that no 
great difference prevails." 

The same author, in Silent Reading in Rural and Village Schools, 
Louisiana State Department of Education, Bulletin No. 9, July, 1919, 
reports results from work with Monroe's Standardized Silent Reading 
Tests with 4,315 pupils in 96 schools located in 15 parishes. He con- 
cludes (p. 8) that "A comparison of the three groups A, B, and C 
reveals a distinct difference in favor of the larger school. With the 
exception of the fourth grade the scores of group B are better than 
those of group C. Group A scores are higher in every instance than 
groups B and C. This superiority of the large type of school is in 
agreement with results reported for Santa Clara County, California." 

Still later, in A Study of Arithmetic in Rapides Parish, Louisiana 
State Department of Education, Bulletin No. 11, September, 1919, Mr. 



14 Study of Achievement in Country and Tozun Schools 

Foote reports results for the use of the Courtis Arithmetic Test Series 
B in the schools of Rapides Parish, Louisiana. In this study schools 
are grouped in four classes, those in the city of Alexandria in group 
A, eight high schools in group B, eight graded schools in group C, and 
twenty-eight one- and two-teacher schools in group D. Mr. Foote 
concludes (p. 12) that "Superior results are obtained in the large type 
of schools." (p. 13.) "Group A and D vary in speed by 1.0 year 
and in accuracy by 2.0 years. It is therefore evident that the large 
schools as represented by groups A and B obtain results that are dis- 
tinctly superior to those obtained by groups C and D." 

George A. Grim, in "Spelling in Northampton County," University 
of Pennsylvania Bulletin, Vol. XX, No. 1, October, 1919, Sixth An- 
nual Schoolmen's Week Proceedings, reports spelling results for the 
rural and urban sections of Northampton County. The results are 
reported for grades 2 to 8 inclusive, and in five of the seven grades 
reported the urban schools surpass the rural. The differences re- 
ported are not great in any case. 

Cyrus D. Mead, in The Spelling Ability of the Plumas County Chil- 
dren, California State Board of Education, Supplement of California 
Blue Bulletin, December, 1919, reports on the spelling ability of the 
pupils of Plumas County, California, as shown by a test from the 
Ayres list. He concludes (p. 5) that "The pupils of this county are 
. . . just about of the average ability of city children over the 
country." 

The above references include all the data easily available dealing in 
an objective way with the comparative results of instruction in rural 
and in urban schools. The difficulty of collecting data in rural schools, 
where distance is great and classes small, makes the time element in 
collecting any large number of cases very great and seems to have pre- 
vented the collection of extensive material. The studies reported in- 
clude 2 studies of composition work ; both of these favor the urban 
school. There are 6 studies of handwriting reported, and of these 3 
favor the urban school, 2 show negHgible differences, and 1 favors the 
rural school. Nine studies of arithmetic are reported, and 8 of these 
favor the urban school, while 1 favors the rural school. Four studies 
of reading are reported, and all of them favor the urban school. 
Seven studies of spelling are reported, 3 of which favor the urban 
school and 4 of which find negligible differences. In all 28 studies are 
reported, of which 20 find the results better in urban schools, 6 find 
negligible differences, and 2 find results superior in the rural schools. 



CHAPTER II 
PURPOSE AND SCOPE OF THE PRESENT STUDY 

The studies of results of instruction in rural schools reported in 
Chapter I are in objective terms, and seem to indicate a situation that 
is quite generally inferior to that in cities and towns. All of the com- 
parisons are made, however, upon a grade basis, which assumes that 
the third grade, or the eighth grade, or any other grade should be the 
same in one system as in another. That grades are not in fact equal 
is shown by results. Under the present diversity of conditions it is 
entirely possible that grades should not be equal. 

Particularly is this true in country schools as contrasted with city 
schools. The shorter terms, poorer attendance, and inherent difficul- 
ties involved in the small school make it probable that grading in these 
schools should be different from that in city schools. For example, 
in Madison County, Kentucky, the school year for the smaller schools 
is only six months. This means that a boy or girl entering school at the 
age of six and progressing normally would at the age of fourteen com- 
plete the eighth grade, having attended school a total of 48 months. A 
child entering one of the larger schools of the country, such as that in 
Richmond, would have nine months' schooling each year, and would, 
if he progressed normally, complete the eighth grade with a total of 72 
months in school ; that is, with 24 months' more schooling than the 
country child received. 

Again, in some of the states the school system is organized on the 
basis of seven grades in the elementary school, so that a direct compar- 
ison of a fifth grade in a seven grade system with a fifth grade in an 
eight grade system is impossible. 

Further, the use of grade standards must assume that tests are given 
at the same time in the school year. This would be necessary either 
to compare the system tested with another system or with the work 
in the same system in other years, since the standard for any grade 
must be different at the beginning and at the close of the school year. 
It is not always convenient, or even possible, to give tests in any partic- 
ular part of the school term. There will be material gain in the ease 
of using standard tests if it can be made possible to give them at any 
convenient time and to obtain results comparable with those from other 
places and given at other times. 

15 



16 Study of Achievement in Country and Tozvn Schools 

Then, too, in any system of schools some pupils are likely to fail of 
promotion each year. This causes retardation, and is much more se- 
rious in some systems than in others. Any consideration of the effi- 
ciency of a school system must account for this factor. Grade stand- 
ards do not do so. 

It is for such reasons as these that the Nassau County Survey, pub- 
lished as a bulletin of the University of the State of New York (De- 
cember, 1917), in reporting the measurements of the achievements of 
pupils, carefully refrains from making any comparison of the urban 
and rural schools, and makes the following statement (p. 146) : "The 
classification of school districts by the approximate size of the schools 
has not been continued in this chapter, because of the possible injus- 
tice which might thereby be done to the small schools, in which the 
exact classification of pupils into eight grades is not always possible. 
There might have been possible a more accurate comparison of the 
results from large and from small districts, if the results had been 
tabulated by age rather than by school grade. A comparison of the 
ability children have in a rural school by the time they are 'twelve 
years old' with the ability of children of the same age in a large village 
school might possibly be more significant than a comparison of the 
ability between children of the 'sixth grade' in the two types of schools. 
For several reasons, however, we have not been able to make such 
comparisons between the achievements of pupils of the same ages in 
districts of various sizes." 

To really measure school efficiency it is necessary to show the prog- 
ress, not only of those who are promoted, but of all the children ; and 
to do this in terms of some unit common to all schools, city or country, 
seven grade or eight grade system, and long or short school term. 
There will be added convenience if such a unit can be so devised as 
to be usable at any time during the school year. 

The chronological age of school children is such a unit. If the prog- 
ress made by children can be shown, say between the ages of 7 and 12, 
a measure that is definite, universal, and approximately equal at any 
time during the school year is obtained, provided only that children of 
both ages are tested at the same time. The question is whether such 
progress can be shown. 

This study undertakes: 

First, to show that the difference in performance in school subjects 
of children of different ages can be obtained ; 



Purpose and Scope of Present Study 17 

Second, to show that this difference is a measure of school efficiency 
which may be used to measure schools or school systems ; 

Third, to apply this measure to a system of country schools ; 

Fourth, to compare the results in this country system of schools with 
the results in certain city school systems. 

The country school system to which this measure is applied is that 
of Madison County, Kentucky. This county lies a little east of the 
central portion of the state, and includes both blue-grass and mountain 
land. In the 1910 census it ranks 20th in the land area among the 
counties of the state, 5th in the value of all farm property, and 12th 
in the value of all farm crops. Corn and tobacco are easily the lead- 
ing crops. The county is one of the wealthier and larger counties of 
the state. There are two normal schools, the Eastern Kentucky State 
Normal at Richmond and a normal department in connection with 
Berea College at Berea. The number of public white schools is 68, 
six of which have three or more teachers and a term of nine months. 
The rest of the schools have only one or two teachers and a six-month 
school year. A county supervisor of schools is employed to assist the 
county superintendent. There is no reason to suppose that the schools 
of this county are particularly worse than those of surrounding counties. 

For the purposes of this study three tests were selected : Trabue 
Completion-Test Language Scale B, Courtis Standard Research Tests 
in Arithmetic Series B, and Thorndike Silent Reading Scale Alpha 2. 
These tests were given in grades 3 to 8 inclusive of all the public 
schools for white children in the county during November and Decem- 
ber, 1919.1 The results are tabulated separately for the schools hav- 
ing a six-month term and for those having a nine-month term. 

In order that the results in Madison County may be compared with 
results in other places, data are included as follows : From Louisville, 
Kentucky, data for each of the three tests used ; from Paterson, New 
Jersey, and St. Paul, Minnesota, data for the Trabue Language Scale ; 
from Louisiana, Arkansas City and Salina, Kansas, and Hibbing, 
Minnesota, data for the Courtis Standard Research Tests in Arithme- 
tic Series B ; from Hamilton Township, New Jersey, and Amsterdam, 
New York, data for Thorndike Silent Reading Scale Alpha 2. 

In order to show clearly the method followed, the results of the 
Trabue Completion-Test Language Scale B are worked through in de- 
tail in the next chapter. 



^ Five of the one-teacher schools were not in session when visited, and no re- 
sults from them are given. 



CHAPTER in 
ACHIEVEMENT MEASURED BY THE TRABUE LANGUAGE SCALE 

Table I shows the age-grade distribution of scores made in the 
Trabue Language Scale B by pupils in the Madison County schools 
having a term of 6 months. The table reads as follows : There are 
8 pupils 7 years of age in the third grade, 1 of whom made a score of 
3, 2 a score of 4, 2 a score of 5, 3 a score of 6, etc. In this table and 
throughout the study the age used is that of the last birthday at the 
time the test was given. A child is considered as 10 years old who is 
as much as 10 years old and less than 11 years old. 

It is evident from the total number of cases occurring for the re- 
spective ages that the distributions are incomplete for most ages ; prob- 
ably for all. There should be at least as many 8-year-old children, for 
example, as there are 9-year-olds. This incompleteness for the younger 
ages represents children in the first and second grades, which were not 
tested, or children who have not yet entered school. Since these chil- 
dren have not yet been promoted to the third or higher grades, it is 
evidently the opinion of the teachers that they could not do so well as 
the children who are in the third or higher grades. It follows that the 
distributions for children of the younger ages are lacking in the num- 
ber of cases for the lower scores. The distributions for the older 
children, on the other hand, may be considered as lacking in the num- 
ber of cases for the higher scores, since the older children not appear- 
ing in the table are those who have either completed the eighth grade 
before reaching the age indicated, or who have for some reason stopped 
attending school. 

If the difference in performance in school subjects of groups of 
children of different ages is to be a valid measure of the efficiency of 
a school system, it is evident that the age-groups in the respective sys- 
tems jnust be comparable. That is to say, either these groups must 
include all children of the age indicated, or the selection must be shown 
to be by random sampling only, or the selection must be shown to be 
influenced only by known causes acting equally and in the same direc- 
tion, or it must be possible to so correct the age-groups given as to 
meet substantially the above conditions. 

The age-groups presented in Table I do not meet the first of these 

18 



TABLE I : Age-Grade Distribution of Trabue Language Scale B Scores in 
THE 6-Month White Schools of Madison County, Ky. (November and 
December, 1919) 



Age 


Grade 


Scores 


Total 







1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 




7 


3 
4 
5 






1 


2 
2 

1 


2 

1 


3 

1 
1 


























8 




1 






1 
























6 
































2 





































Total 




1 






1 


5 


3 


5 


1 
























16 






























8 


4 
5 


6 
1 




2 
1 


1 

1 


3 
3 


2 

1 


10 

7 
1 


'"4 


2 
1 
4 


1 




















27 


1 


1 






1 










22 












5 






































Total 




7 




3 


2 


6 


3 


18 


4 


7 


1 


1 


1 






1 










54 














g 


3 
4 
5 


6 
6 




6 
2 
1 


"i 


12 

1 


2 
3 


9 

7 
4 


3 
2 


2 
3 

7 






















40 




3 
4 


2 
1 


3 


.... 


1 
1 












33 














20 
















Total 





12 




9 


1 


13 


51 20 


5 


12 


7 


3 


3 


1 


2 












93 














10 


3 
4 
5 
6 

7 
8 


3 
1 


1 


1 


1 


5 
3 

2 


1 
3 


9 
6 
4 
1 
1 
1 


1 
2 
4 
2 


i 
8 
3 
2 


'"3 
5 
1 


1 
2 
3 
1 


2 
3 
4 
2 


1 
.... 














30 




1 
2 












31 






2 














32 




1 











11 
























1 




























1 












2 









































Total 




4 


1 


■? 


1 


10 


6 


22 


9 


17 


9 


7 


11 


9 


4 


1 








107 


















11 


3 

4 
5 
6 

7 
8 


3 
1 




3 
1 

1 




3 
3 

2 


3 
2 


5 
10 

3 

1 


2 
1 
3 


1 
2 
4 
1 
2 


1 
4 
3 


3 
4 
5 
1 


.... 

5 
2 


1 
1 

4 
1 
1 














19 














28 




2 












34 






2 

1 


2 




.... 


16 


















5 






















1 




1 




2 






































Total 




4 




5 




8 


6 


19 


6 


10 


8 


13 


8 


8 


2 


1 


3 


2 


1 




104 


12 


3 
4 
5 
6 

7 
8 


1 
1 


1 


1 




1 
1 
2 


1 

1 


3 
9 

8 

1 


2 

4 

3 

.... 
























10 




3 
5 
3 


6 

2 

6 

2 

1 


.... 

5 
1 


"2 
4 
2 


1 
4 
4 
7 
2 














25 










2 
1 

2 












31 






- 


1 


___ 


1 
1 
1 










27 












16 




















3 


.... 




7 






1 






















Total 




2 







A 


4 


91 


in 


11 


17 


7 


8 


18 


6 


3 




■^ 






116 
















13 


3 
4 
5 
6 

7 
8 


1 




3 

1 




1 
1 


"i 
1 

1 








1 

2 

4 
5 




















6 




2 
6 


1 

4 
2 
2 
1 


2 
2 
6 
2 

i 


2 
2 
1 

'"2 


.... 


1 


--- 


.... 


... 






16 
27 












2 
3 
1 


2 

'"4 


1 
2 
5 










23 














2 








12 


















1 




16 




2 




















Total 






4 




2 


3 


14 


9 


10 


12 


13 


7 


6 


7 


8 


2 




1 




100 


14 


3 
4 

5 
6 

7 
8 


"2 




"\ 




1 
1 






.... 

2 
2 


'""5 
2 

1 
2 
2 


1 

'"2 
3 
2 
2 




















3 




1 

2 

1 

.... 


















11 




3 
3 

2 
2 


1 
.... 

1 


3 

2 
6 


1 

I 
5 










18 


















15 




1 












1 
2 








13 




1 




















22 
























Total 




3 


1 


1 




2 




5 


5 


12 


10 


5 


10 


3 


13 


9 


3 








82 












15 


3 
4 
5 
6 

7 
8 












1 




1 
























2 














1 


1 


1 


















3 














1 


.... 


— - 


















2 
















1 
1 
4 


1 
1 
1 






1 
1 

2 










3 
























3 

2 


""3 










6 






















1 


3 


1 


.... 




17 
























Total 










__ 




2 




1 


2 


2 


7 


3 


5 


3 


4 


3 


1 






33 


16 


4 
5 
6 
7 
8 









■ 




■ 




1 
























1 


















2 






















2 


































































2 

1 


3 
1 


3 
4 


1 










9 












1 










1 


4 


4 








16 




























Total 












1 






1 


2 


1 


4 


3 


4 


7 


1 


4 








28 



19 



20 Study of Achievement in Country and Tozvn Schools 

conditions, in that they do not include all the children of the ages 
indicated. Take, for example, the group of 12-year-old children, the 
largest group presented. This shows 10 children in the third grade, 
25 in the fourth, 31 in the fifth, 27 in the sixth, 16 in the seventh, and 
7 in the eighth. Since the distribution of 12-year-old children through- 
out the grades is not rectilinear, as is shown by the part of the distri- 
bution given, it seems unlikely that if a full distribution were available 
it would stop at the lower end with 10 children in the third grade or 
at the upper end with 7 children in the eighth grade. It seems likely 
that there would be some 12-year-old children in grades below the 
third and in grades above the eighth. This opinion in the latter in- 
stance is substantiated by the fact that some 10- and 11-year-old chil- 
dren are in the eighth grade this year. If they progress normally, 
they will complete the work of the elementary school this year, and 
will not be enrolled in the school next year. The same thing is likely 
to have happened last year, so that there are now some children who 
are 12 years old and have completed the work that the school offered 
and are therefore not in school. Also, there are 13-, 14-, and even 15- 
year-old children in the third grade. There is every reason to sup- 
pose that there are 12-year-old children in grades lower than the third. 
In addition to the above considerations, it is known that there were 
some children absent from school on the day the tests were given. 

As regards the second possibility mentioned for comparable groups : 
Is the selection by random sampling only? In so far as the selection 
is due to absence from school on the day the test was given, the se- 
lection may be considered random as to ability in the test concerned. 
The chief causes of absence mentioned by the teachers were work, bad 
weather, illness, and indifference on the part of the parents. The 
work for which the children were kept at home during the time these 
tests were being given (November and December) was usually work- 
ing tobacco or killing hogs. While it is likely that more of the older 
children than of the younger ones were kept at home for work, still 
some of the younger ones were kept at home for this purpose. The 
discrepancy in absences between the older and younger children in re- 
gard to absence for work is reversed and probably neutralized by the 
discrepancy in absences due to bad weather and roads. The absences 
due to illness of the children and to indifference on the part of the 
parents may be assumed to be about the same for children of all ages. 

On the other hand, the selection due to the inclusion of only those 
children in grade 3 to 8 inclusive is not random. The older children 



Achievement Measured by Trabue Language Scale 21 

in grades 1 and 2, that is, those who are not included in the distribu- 
tion given, are in those grades because, in the opinions of the teachers, 
they are not so able as the children of the higher grades, or because 
they have for some reason become so retarded in their school work as 
to make them distinct from other children. In other words, these 
children are, in the opinions of the teachers, of less ability in school 
work than those of corresponding age who have been promoted to the 
higher grades. This means that the distributions given in Table I 
do not include the children who have the lower degrees of ability in 
school work. In the same way the younger children who have com- 
pleted the eighth grade and are therefore not included in the table are, 
in the opinions of the teachers, the children having the higher degrees 
of ability in school work. All of which goes to show that the selec- 
tion of cases for the age-groups as they are presented is not random. 

The next consideration is whether the selection of age-groups, in 
such respects as it is not random, is due to the same causes acting 
equally and in the same direction, for all the schools to be measured, 
and in each of the age-groups. As is shown above, there is decided 
selection due to the failure to include children in grades 1 and 2, and 
those who have completed the eighth grade. This number of children 
is determined by the rate of progress of children through the grades. 
This rate of progress is unequal even for different schools within the 
same system, as has been shown repeatedly by studies widely sepa- 
rated both in time and locality. A good and recent example is fur- 
nished by the age-grade tables on page 90 of An Educational Study of 
Alabama, United States Bureau of Education Bulletin, 1919, No. 41. 

The possibility still remains of correcting the tables presented. In 
order to correct an incomplete distribution such as that presented it 
is necessary to have a reasonably large part of the complete distribu- 
tion. In the data presented the most nearly complete distributions are 
those for the ages 10, 11, 12 and 13. The distribution of 12-year- 
olds is the largest given, which indicates that it is most nearly complete. 
Taking this distribution as a sample, how may it be corrected ? 

Unfortunately the form of this distribution is not exactly that of 
the normal frequency curve. This is shown by that portion of the 
distribution which is given. It might also be inferred from the fact 
that in most school systems it is easier for a child to become retarded 
than it is for a child to make two grades in one year.^ This natu- 



^ Strayer and Thorndike, Educational Administration, p. 38. 



22 Study of Achievement in Country and Tozvn Schools 

rally causes a skewed distribution. To correct a skewed distribution for 
truncation by the development of mathematical formulae is a lengthy 
and complicated process, and one that is liable to serious error. Fur- 
ther, since the degree of skewedness and of truncation may both vary 
for every distribution to be studied, such correction is obviously too 
tedious and cumbersome a method to be used in a measure of school 
efficiency that is to be easily available for busy school men. 

If an age-grade table of all the children in all the grades were avail- 
able, it might serve as a basis for calculating the number of children in 
grades 1 and 2. It does not furnish a ready basis for finding the num- 
ber who have completed the eighth grade. Also, for Madison County 
schools no such table is available.' 

The problem resolves itself into an attempt to find the number of 12- 
year-old children who are in either the first or second grade, or who 
have completed the eighth grade. The 13-year-old children in the 
third grade this year probably were in the second grade last year when 
they were 12 years old. The probability is that last year the number 
of 12-year-old children in the second grade who were not promoted 
to the third grade was about equal to the number of 13-year-old chil- 
dren in the third grade who were not promoted to the fourth grade. 
Inasmuch as there has been no particular change in the school popu- 
lation of Madison County during the last few years, and in view of 
the above probabilities, the number of 13-year-old children in the 
third grade may be considered a fairly reliable indication of the num- 
ber of 12-year-old children in the second grade.- Reference to Table 
I shows this number to be 6. Similarly, the 14-year-old children in 
the third grade may be considered a measure of the 12-year-olds in 
the first grade. This number is 3. 

In much the same way it may be supposed that the number of 11- 



^To get a census showing the ages of children in the first and second grades 
of the Madison County public schools it would be necessary to visit each school, 
and in the case of children who do not know their age, to visit the home. 

" In order to test the validity of this assumption a study was made of the 
age-grade tables for rural children and for children in places having a popula- 
tion of less than 2,000 given on page 90 of An Educational Study of Alabama, 
United States Bureau of Education Bulletin, 1919, No. 41, and the age-grade 
table for pupils in non-city schools given on page 309 of the Survey and Report 
of the Virginia Public Schools Education Commission. The actual number of 
10-, 11-, 12- and 13-year-old children in grades 1 and 2 was compared with the 
number of such children estimated to be in these grades on the basis of the 
above assumption. The difference between the actual number of such children 
and the estimated number was reduced to a percentage basis showing the per 
cent of error in each estimate. Twenty-four estimates were made, and the 
median per cent of error, direction of error being taken into account, was — 4^. 



Achievement Measured by Trabue Language Scale 23 

year-old children in the eighth grade this year is the same as the num- 
ber of 11-year-old children in the eighth grade last year. These should 
be added to the 12-year-old distribution this year. Reference to Table 
I shows this number to be 2. In the same way the number of children 
who are 12 years old this year and who completed the eighth grade 
two years ago is estimated as 2. 

Using these estimates, the following distribution of 12-year-old chil- 
dren is obtained: 3 in grade 1, Language Scale scores unknown; 116 
in grades 3 to 8 inclusive, distributed according to Language Scale 
scores ; 2 who completed grade 8 last year, Language Scale scores un- 
known; and 2 who completed grade 8 two years ago. Language Scale 
scores unknown. 

Estimating corrections for the 10-, 11- and 13-year-old distributions 
on the same basis as for the 12-year-olds, gives Table IL In this 
table the figures in the columns under the captions XI, X2, X9, XIO, 
and XI 1 are the estimated number of children of the respective ages 
in grades 1, 2, 9, 10 and 11 respectively.^ 

These corrections make the distributions for the ages 10, 11, 12 and 
13 reasonably complete. There is still some elimination of children in 
the grades to be accounted for, and there is the possibility that some 
of the children of these ages may not have entered school. These 
considerations are probably not so serious, however, as the fact that 
the scores of the children represented by estimated additions to the 
distributions are unknown. It is known, however, that the children 
in the lower grades are likely to have made very low scores, while, 
on the contrary, the children who have completed the eighth grade 
would probably have made relatively high scores. Allowing these 
cases to remain undistributed at the respective ends of the distribution, 
the medians, Q's and P.E.'s of Table II are obtained. 

The distributions of scores in this table show a great amount of 
overlapping for the different ages. Twenty per cent of the children 
in the 10-year-old group have scores superior to those of 50 per cent 
of the 13-year-old children. This overlapping is in accord with the 
results obtained with grade distributions. 



^ An attempt was made to estimate the necessary additions for these distribu- 
tions on the basis of an age-grade table showing a form of distribution similar 
to that in Madison County. The age-grade table for the Alabama schools in 
places of less than 2,000 population was used. No estimate of children who 
had completed the eighth grade seemed feasible on this basis, and the medians 
calculated on the basis of the distributions corrected in this way showed co- 
efficients of unreliability greater in every instance than those of the medians cal- 
culated on the basis of the above corrections. 



24 Study of Achievement in Country and Town Schools 



As in the overlapping of grade distributions, so in this overlap- 
ping with age distributions, the unreliability of the individual measures 
gives an indication of greater overlapping than really exists.^ In this 
case there is an added element tending to exaggerate the amount of 
overlapping in the undistributed scores at both ends of the age distri- 
butions. These scores tend to increase the inter-quartile range, and 
consequently the Q. 

TABLE II 

Age Distribution, 10 to 13 Inclusive, of Trabue Language Scale B Scores 

IN THE 6-MoNTH WhITE ScHOOLS OF MaDISON CoUNTY, Ky. 







Scores 










Age 














Total 




XI 

in 


X2 
10 





1 
1 


2 


3 
1 


4 

in 


5 


6 

99 


7 
q 


8 
17 


9 

q 


10 

7 


11 

11 


12 

? 


13 
4 


14 

1 


15 


16 


17 


18 


X9 


XIO 


Xll 




10 








136 


11 


fi 


in 


4 




fi 




8 


6 


11 


6 


in 


8 


13 


8 


8 


2 


1 


3 


2 


1 




2 






122 


n 


3 


fi 


2 


1 


2 




4 


4 


21 


10 


11 


17 


7 


8 


18 


6 


2 




3 






2 


2 




129 


13 


2 


3 


2 




4 




2 


3 


14 


9 


10 


12 


13 


7 


6 


7 


8 


2 




1 




7 


2 


2 


116 






P. E. true 


















Median 


— obtained 
median 


75 per- 
centile 




25 pe 
centil 


r- 
e 


Q 




P. E. 


in 


6.63 


.37 


9.00 




2.00 




3.50 


Mil— M10= .87 


.311 


11 


7.50 


.34 


10.73 




4.68 




3.02 


M12— Mll = 1.52 


.283 


^?. 


9.02 


.30 


12.04 




6.48 




2.78 


M13— M12= .73 


.305 


13 


9.75 


.35 


13.00 




6.92 




3.03 


M13— M10 = 3.12 


.316 



Another notable feature of this table is the great discrepancy be- 
tween progress at different ages. The improvement the 11 -year-old 
children show over the 10-year-olds is .87 of a step ; that of the 12- 
year-olds over the 11-year-olds is 1.52; and that of the 13-year-olds 
over the 12-year-olds is .73 of a step. The progress in language ability 
as measured by this test is almost as great from ages 11 to 12 as the 
combined progress from ages 10 to 11 and from ages 12 to 13. 

The total progress for the three-year period from 10 to 13 inclusive 
is 3.12 with a P.E. of .316.- Since these schools were in session for 
6 months each year, the total school time for the three years is 18 
months. This makes the average progress per month for the period 
.173 of a step. 

The results of the Trabue Language Scale B test in the white schools 
of Madison County having a 9-month school term are handled in the 



^ Thorndike, E. L. : Mental and Social Measurements, p. 93. Kelley, T. L. : 
"The Measurement of Overlapping," Journal of Educational Psychology, X : 
458#. (December, 1919). 

^ Thorndike : Mental and Social Measurements, p. 194. 



Achievement Measured by Trabue Language Scale 



25 



same way as are those from the schools having a 6-month school term. 
Table III gives the facts for these schools. 

From this table it seems that the overlapping of language perform- 
ance of children of different ages is about as great in the 9-month 
schools as in the 6-month schools. Some of the 10-year-old children 
have scores above the median score of the 13-year-olds. The same 
causes are operating to make this overlapping appear greater than it 
really is. 

TABLE III 

Age Distribution, 10 to 13 Inclusive, of Trabue Language Scale B Scores 
IN the 9-Month White Schools of Madison County, Ky. 









Scores 










Age 














Totdl 




XI 

9 
2 


X2 
17 







1 


2 




3 


4 

8 


5 

7 


6 
18 


7 
7 


8 
17 


9 


10 
1'' 


11 

8 


12 

8 


13 

3 


14 
I 


15 
? 


16 
1 


17 
1 


18 


X9 


XIO 


XI 1 




10 








132 


g 


7 




9 


1 


■^ 


^ 


H 


(^ 


16 


5 


8 


1 


7 


4 


S 


? 


1 


1 




1 






101 


n 


3 


? 


S 




2 


1 


fi 


3 


8 


4 


8 


14 


12 


12 


12 


15 


10 


11 


7 


1 


1 


1 


1 




139 


n 


4 


3 


7 










1 


2 


4 


4 


10 


9 


5 


1 


9 


11 


11 


2 


-- 




10 


1 


i 


101 


















p. E. trii 


e 
















Median 


— obtaine 
median 


d 


75 per- 
centile 


25 per- 
centile 




Q 




P.E. 


10 


7.42 


.32 




10.33 


4.37 




2.98 


Mil— M10= .73 


.290 


11 


8.15 


.31 




10.84 


5.31 




2.76 


M12-M11=2.97 


.284 


n 


11.12 


.30 




13.81 


8.09 




2.86 


M13— M12 = 1.09 


.295 


13 


12.21 


.36 




14.97 


9.02 




2.97 


M13— M10=4.79 


.304 



Note. — In these and succeeding tables XI is the estimated number in grade 1, 
scores unknown. X2, X9, XIO and XI 1 represent the corresponding facts for 
grades 2, 9, 10 and 11 respectively. MIO is the median for 10-year-old children, 
age last birthday at the time the test was given. Mil, M12 and M13 are the 
medians for the ages 11, 12 and 13 respectively. 

Also, the progress between the different ages is unequal, as in the 
case of the children in the 6-month schools. The improvement between 
ages 10 and 11 is .73 of a step ; between ages 11 and 12 it is 2.97 steps ; 
and between ages 12 and 13 it is 1.09 steps. The total improvement for 
the three-year period from ages 10 to 13 inclusive is 4.79 steps, with a 
P.E. of .304. Since there are 9 months of school each year, the total 
school time represented is 27 months. The average monthly improve- 
ment, therefore, is .177 of a step. The corresponding improvement 
for the 6-month schools is .173 of a step. 

This comparison would be valid and significant if it could be as- 
sumed that the quality measured, ability to complete correctly sen- 
tences in which certain words are missing, was improved only by school 



26 Study of Achievement in Country and Town Schools 

work. Such, however, is not known to be the case. It is entirely 
possible that this quality improves by a natural development as the age 
and experience of the subject increases. It is possible, and even prob- 
able, that this ability to complete sentences is improved both by natural 
development and by school work. The conclusion from the above 
comparison, therefore, is that schooling and natural development ac- 
complish an improvement of this ability of 4.79 steps between the 
ages of 10 and 13 inclusive for the children in places in Madison 
County having a 9-month school term, and of 3.12 steps in places in 
the same county having a 6-month school term. 



TABLE IV 

Age Distribution, 10 to 13 Inclusive, of Trabue Language Scale B Scores 
IN Certain White Schools of Louisville, Ky. 



Age 






Scores 






Total 




XI 
4 

1 


X2 

12 
4 


X3 

36 
12 


1 


2 


3 


4 

1 
4 


5 

"2 


6 

8 
5 


7 

2 
1 


8 

18 
13 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


X9 




10 


4 
6 


32 
39 


17 
9 


43 
55 


17 
11 


29 
67 


6 
13 


14 
26 


1 
1 


3 
17 








247 


11 


2 








6 




292 


P 




1 


4 . 
1 - 








2 
2 


1 


2 
3 


3 

1 


21 
10 


3 
5 


19 
22 


12 

8 


43 
53 


19 
13 


77 
65 


lb 

27 


70 
46 


4 
6 


27 
20 


4 
1 


4 

7 


"26 


332 


1"? 








316 
















P. E. true 


















Median 


— obtained 


75 per 




25 per- 




Q 




P.E. 









mediad 


centile 




centile 










in 


11.32 


.24 


13.48 




7.37 




3.11 


Mil— M10= 1.58 


.174 


11 


12.90 


.14 


14.37 




10.36 




2.00 


M12— Mll = 1.56 


.120 


1? 


14.46 


.13 


16.37 




12.34 




2.01 


M13-M12= .15 


.120 


13 


14.61 


.14 


16.58 




12.50 




2.04 


M13— M10=3.29 


.174 



Table IV gives the facts in regard to the Trabue Language Scale B 
test for certain of the white schools of Louisville. The papers on 
which this table is based were given, collected and scored by the 
Psychological Laboratory of the Louisville Board of Education. 

The total improvement in ability to complete sentences in these 
schools for the three-year period from ages 10 to 13 inclusive is 3.29. 
The P.E. of this gain is .174, a little over 5 per cent of the gain. The 
probable deviation of the true measure of this gain from the measure 
obtained is only about half as great as in the Madison County schools, 
either those having a 9-month school term or those having a 6-month 
term. The total gain made is a little greater than in the case of the 
Madison County 6-month schools and is not quite so great as in the 
case of the Madison County 9-month schools. The median ability of 
the respective age-groups, on the other hand, is materially higher than 



Achievement Measured by Trabue Language Scale 



27 



is the case in any of the Madison County schools. The median for the 
Louisville 10-year-old children is higher than for any of the age-groups 
of the 6-month schools, and is higher than all except the 13-year-old 
group for the 9-month schools. The median ability of the Louisville 
13-year-old group is 14.61 ; that for the Madison County 9-month 
schools of -corresponding age is 12.21, and for the 6-month schools is 
9.75. The 13-year-old children in Louisville have an ability to com- 
plete sentences that is 50 per cent greater than the like ability of chil- 
dren of the same age in the 6-month schools of Madison County. 

The progress made each year in the Louisville schools is unequal, 
as is the case in the Madison County schools. In Louisville the prog- 
ress from 10 to 11 is 1.58; from 11 to 12 it is 1.56; and from 12 to 13 
it is .15. 

TABLE V 

Age Distribution, 10 to 13 Inclusive, of Trabue Language Scale B Scores 

IN Paterson, N. J. 







Scores 












Age 














Total 




XI 



5 


1 
2 


2 

7 
1 


3 

2 


4 

5 
6 
5 


5 

4 
4 

2 


6 

23 
11 

8 


7 

18 
10 

8 


8 

31 
17 
15 


9 

20 
16 
16 


10 

34 
34 
39 


11 

23 
27 
19 


12 

15 
29 
32 


1 

1 

1 
2 


3 14 

3 4 
8 11 
5 18 


15 

2 
4 
9 


16 


17 


18 


19 


X9 


XIO 




10 


1 
7 
9 












209 


n 


2 
3 


2 
3 


1 

1 






200 


12 





1 




8 




224 


ii-t 










1 


1 


2 


6 


2 


14 


13 


25 


20 


29 


2 


6 17 


16 


12 


9 


1 




42 


8 


246 
















P. E. true 




















Median 


— obtained 




75 per- 


25 per- 




Q 






P.E. 






median 




centile 


centile 












10 


9.03 


.12 




10.01 


7.02 




1.49 




Mll-M10=2.27 


.128 


11 


11.30 


.16 




12.82 


9.06 




1.88 




M12— Mll= .48 


.141 


12 


11.78 


.16 




13.80 


9.87 




1.96 




M13— M12 = 1.52 


.180 


13 


13.30 


.24 




16.87 


10.82 




3.02 




M13-M10=4.27 


.170 



Table V gives the facts in regard to the Trabue Language Scale B 
for schools in Paterson, New Jersey. The data from which this table 
is compiled were collected by the department of school administration 
of Teachers College, Columbia University. 

The total gain in ability to complete sentences in the Paterson schools 
is 4.27. This gain is greater than in the case of any other schools pre- 
sented in this study. The P.E. of this gain is .170, which is about the 
same as that for the like measure in Louisville. Since the gain in this 
case is greater, the proportion of the probable error to the gain is a 
little less; in Paterson 4 per cent as against a little more than 5 per 
cent in Louisville. The median ability of the 13-year-old children in 
the Paterson schools is 13.30 as against 14.61 in the Louisville schools. 



28 



Study of Achievement in Country and Town Schools 



CHART I 
Progress in Trabue Language Completion Test Scores Between Age 
Groups in the Public Schools of Madison County, Ky. ; Louis- 
ville, Ky. ; Paterson, N. J.; and St. Paul, Minn. 

SCORES 
16 



15 

14 

13 

12 

II 

(0 

9 

8 

T 

6 

5 

4 

3 

2 

I 


AGES 10 





MADISOR COUNTY 
9-MONmSCMOOLS 



MADISON^tlf 
e-NONTfiSCHOOLS 



12 



13 



Achievement Measured by Trabue Language Scale 



29 



This median ability of the 13-year-old children in Paterson, however, 
is greater than is the like measure for the 6-month or the 9-month 
schools of Madison County. 

The yearly gains are again unequal. From 10 to 11 the gain is 
2.27; from 11 to 12 it is .48; and from 12 to 13 it is 1.52. 

Table VI gives the facts in regard to the Trabue Language Scale B 
in St. Paul, Minnesota. This table is based upon data printed in the 
St. Paul Survey. 

TABLE VI 

Age Distribution, 10 to 13 Inclusive, of Trabue Language Scale B Scores in 
St. Paul, Minn. Based on Tables Published in the St. Paul Survey 



Age 


Scores 


Total 


10 




4 

1 


1 


2 

15 
2 

1 
2 


3 

4 
1 
1 
1 


4 

19 
8 
3 
5 


5 

9 
6 
4 

1 


6 

30 
24 
13 
10 


7 

24 
8 
13 
11 


8 

56 
39 
42 
21 


9 

33 
25 
21 
16 


10 

63 
53 
55 
41 


11 

41 
30 
39 
39 


12 

52 
53 
77 
61 


13 

" 26 
35 
45 
54 


14 

24 
50 
50 
66 


15 

12 
8 
30 
40 


16 

4 
11 
20 
29 


17 

1 
3 
4 
14 


18 


19 


X9 


417 


11 
12 
13 


'"■4 

7 


2 
.... 


"38 


359 
422 
453 




Median 


P. E. true 

—obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 
11 
12 
13 


10.32 
11.41 
12.24 
13.34 


.13 
.14 
.11 
.12 


12.28 
13.55 
14.05 
15.29 


7.96 
9.03 
10.13 
11.13 


2.25 
2.26 
1.96 
2.08 


Mil— M10=1.18 
M12— Mll= .83 
M13— M12 = 1.10 
M13-M10=3.11 


.120 
.106 
.098 
.106 



The total gain in ability to complete sentences in this case is 3.11. 
This gain is less than in any of the other systems studied. The median 
ability of the 13-year-old children, on the other hand, is 13.34, which 
is higher than the like ability of the same age-group in any of the other 
systems studied except Louisville. The P.E. of the gain in these 
schools is .106, which is less than 4 per cent of the gain made. The 
reliability of the measure in St. Paul seems a little greater than in any 
of the other systems considered. The progress from age to age is un- 
equal. From ages 10 to 11 it is 1.18; from ages 11 to 12 it is .83 ; and 
from ages 12 to 13 it is 1.10. 

Chart I shows the progress for the different systems both relatively 
and absolutely. It is significant that while the progress in the Madison 
County schools having a 9-month school term is relatively a little 
greater than the progress in the city schools presented, the total result 
is less. In other words, although the children gain as much or a little 
more in ability to complete sentences between the ages of 10 and 13, 
they have less of this ability when they began and less when they get 



30 



Study of Achievement in Country and Town Schools 



through. This would seem to indicate either later entrance in school 
or poorer work with the lower grades, possibly both. 

The following table summarizes the total gain in ability to complete 
sentences, as measured by the Trabue Language Scale B, between the 
ages of 10 and 13, for the respective school systems considered. It 
also shows the P.E. of this total gain, and the number of cases on 
which this measure of gain is based. 



School Systems 


Total 

GAIN 


P.E. OF 

TOTAL 

GAIN 


Total 
frequencies 




10 to 13 


10 and 13 


Madison County, 6-month schools 

Madison County, 9- month schools 

Louisville 


3.12 
4.79 
3.29 
4.27 
3.11 


.316 
.304 
.174 
.170 
.106 


252 
233 
563 


Paterson . .. _ 


455 


St. Paul 


870 







It should be noted that the reliability of the gains given, as indicated 
by a relatively small P.E., is much greater in the city schools than in 
the Madison County schools. This is due in part to the greater num- 
ber of cases. That it is not wholly due to this cause is indicated by 
the fact that the reliability is greater for the Madison County 9-month 
schools than for the 6-month schools, though the number of cases is 
slightly less. It is possible that this greater reliability is due in part 
to a more uniform type of work in the city and town school systems 
than in the country schools. 

It is also to be noted that the combination of elimination, natural 
development and schooling over a three-year period increased the ability 
to complete sentences 4.79 steps in places in Madison County having 
a 9-month school term,. 4.27 steps in Paterson, 3.29 steps in Louisville, 
3.12 steps in places in Madison County having a 6-month school term, 
and 3.11 steps in St. Paul. If it may be assumed that the amount of 
this increase due to natural development is the same in all these places, 
the efficiency of the schools in training and eliminating children be- 
tween the ages of 10 and 13 in such ability in language as is measured 
by the Trabue Language Scales would rank in the above order. 

This ranking does not agree with that obtained by ranking in order 
of the median ability of the 13-year-old children. Ranking in this 
way, Louisville comes first with a median of 14.61, St. Paul second 
with 13.34, Paterson third with 13.30, Madison County 9-nionth schools 
fourth with 12.21, and Madison County 6-month schools last with 9.75. 



Achievement Measured by Trabue Language Scale 



31 



This discrepancy may be due to a difference in the work with chil- 
dren under 10, to a greater irregularity of attendance of the younger 
children in some systems than in others, to a difference in the amount 
of gain due to natural development because of different environment, 
to a difference in care in scoring papers, to a difference in intellectual 
level of the communities, or to a combination of these causes. 

The following table shows the yearly gains in each of the systems 
of schools studied : 



School Systems 




Yearly Gains 






10 to 11 


11 to 12 


12 to 13 


Madison County, 6-month schools _ . _ 


.87 

.73 

1.58 

2.27 

1.18 


1.52 
2.97 
1.56 

.48 
.83 


.73 


Madison County, 9-month schools.. 


1.09 


Louisville 


.15 


Paterson . 


1.52 


St. Paul 


1 10 






Total .... . ... ... 


6.63 


7.36 


4.59 







This table seems to indicate that the greatest gain is made from 
ages 11 to 12, but that material gain may be made during any of the 
yearly periods from ages 10 to 13 inclusive. 



CONCLUSIONS 

1. The difference in performance as measured by the Trabue Lan- 
guage Scale B of school children of different ages can be obtained. 

2. Since this test measures a quality not proved to be solely, or even 
largely, determined by school training, this difference is not a reliable 
measure of school efficiency. 

3. This difference does measure the improvement of children in the 
respective systems as to the function measured, such improvement be- 
ing due to school training and other influences. 

4. The children in the Madison County 6-month schools show less 
improvement during the three-year period from 10 to 13 inclusive than 
do the children in any of the other systems except St. Paul. 

5. The 13-year-old children in the Madison County 6-month schools 
show less ability in the function measured than do the children of like 
age in any of the other systems studied. 

6. The children in the Madison County 9-month schools show rea- 
sonable improvement during the three-year period from 10 to 13 in- 



32 Study of Achievement in Country and Tozvn Schools 

elusive, but the ability of the 13-year-old children to complete sen- 
tences is less than the like ability of 13-year-old children in any of the 
systems studied except the 6-month schools in the same county. 



CHAPTER IV 

ACHIEVEMENT AS MEASURED BY THE COURTIS STANDARD 
RESEARCH TESTS IN ARITHMETIC SERIES B 



At the same time that the Trabue Language Scale B was given in 
the schools of Madison County, the Courtis Standard Research Test 
in Arithmetic Series B was used. 

The problems involved in finding the difference in performance of 
different age-groups are practically the same as in the work with the 
Trabue Language Scale B. Distributions for the respective age- 
groups are completed on the same assumptions, and the same age- 
groups are used throughout. The number of examples correctly com- 
pleted has been used as the score. 

The work in addition, subtraction, multiplication and division is 
presented in sections 1, 2, 3 and 4 respectively of this chapter. 

Section L Addition 
Table VII gives the data in addition for the children 10 to 13 years 
of age inclusive in the Madison County schools having a 6-month term. 
A new problem is presented in this table in that the medians of the 

TABLE VII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Addition Rights in the 6-Month White Schools of Madison County, Ky. 





Scores 




Age 




Total 




XI 


X2 




65 
54 
62 
45 


1 


2 


3 


4 


5 


6 


7 


8 


9 


X9 


XIO 


XU 




10 


11 
5 
3 

2 


19 
11 
5 
3 


25 
20 
19 
16 


9 
12 
19 
13 


7 
10 
5 
8 


6 

6 

7 

11 




1 
2 
4 


1 












144 


11 


4 
8 
5 






2 
4 
13 






126 


12 


2 






2 
4 




140 


13 




1 


2 


123 
















P. E. true 














Median 


— obtained 
median 


75 per- 
centile 


25 per- 
centile 


Q 




P. E. 


10 


.64 


.07 


1.52 


.09 


.71 


Mil— M10= .23 


.072 


11 


.87 


.11 


2.37 


.28 


1.04 


M12— Mll= .13 


.092 


12 


1.00 


.12 


2.48 


.43 


1.20 


M13— M12= .71 


.147 


13 


1.71 


.21 


4.47 


.57 


1.90 


M13— M10=1.07 


.136 



10- and 11 -year-old groups fall in the to 1 interval, and that the 25 
percentiles of all age-groups fall in the same interval. It may be 



33 



34 Study of Achievement in Country and Town Schools 

questioned whether the children in grades 1 and 2, grouped under 
the captions XI and X2, should be considered as having a score of 0, 
or whether an attempt should be made to distribute their scores. Tab- 
ulation of the pupils' test papers shows that there are 147 children in 
grade 3, and that 127 of these grade 3 children made a score of 0. 
Since 127 out of 147 children made a score of and since it may be 
safely assumed that children in grades 1 and 2 would not do so well 
as children in grade 3, the score of these first and second grade chil- 
dren has been considered as 0. Scores given under the caption have 
been considered as distributed evenly between and 1. 

The large number of scores in the to 1 interval as well as the 
scores considered as indicate that the ability in addition required to 
do any of the examples in the Courtis Standard Research Tests in 
Arithmetic Series B is so great as to preclude measurement of many 
of the individuals tested further than to show that their ability is less 
than the lowest ability measured by this test. The great number of 
cases also reduces Q. 

TABLE VIII 
Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Addition Rights in the 9-Month White Schools of Madison County, Ky. 







Scores 








Age 










Total 




XI 


X2 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


X9 


XIO 


Xll 




10 


9 
1 
3 


16 
9 

1 


23 
21 
21 


14 
13 
19 


19 
12 
15 


11 

7 
24 


16 
10 
17 


6 

7 


5 
9 
13 


5 
2 
6 




1 

2 


1 


1 
3 
1 








127 


11 


1 
1 






94 


12 


2 1 




1 




131 


13 


4 


3 


7 


15 


11 


11 


17 


8' 


5 


3 




2 1 




1 


8 


1 


1 


98 






P. E. true 














Median 


— obtained 
median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 


2.07 


.21 


4.20 


.26 


1.97 


Mil— M10= .18 


.206 


11 


2.25 


.26 


4.75 


.64 


2.05 


M12— Mll = 1.02 


.194 


12 


3.27 


.19 


4.89 


1.40 


1.74 


M13— M12= .54 


.186 


13 


3.81 


.25 


5.68 


1.70 


1.99 


M13— M10 = 1.74 


.198 



The total gain in ability to add for the three-year period from ages 

10 to 13, as measured by the difference in the median scores of the 
10-year-old and the 13-year-old children who took the test, is 1.07, 
with a P.E. of .136. This P.E. is slightly over 12 per cent of the total 
gain indicated. 

The improvement in ability to add from year to year, as measured 
by the difference between the median scores of the respective age- 
groups, is uneven, as it is in the case of language. From ages 10 to 

11 the improvement is .23; from ages 11 to 12 it is .13; and from ages 



\ 



Achievement Measured by Courtis Arithmetic Tests 



35 



12 to 13 it is .71. The improvement from ages 12 to 13 is practically 
twice as great as the combined improvement from ages 10 to 11 and 
from ages 11 to 12. Apparently the first real teaching of such ability 
to add as is measured by the Courtis Standard Research Tests in Arith- 
metic Series B in these schools is to children between the ages of 12 
and 13. 

Table VIII presents the facts in regard to addition in the 9-month 
schools of Madison County. The same statistical method is used as 
that used with the data from the 6-month schools. 

The total improvement in ability to add in these schools for the 
three-year period from ages 10 to 13 inclusive is 1.74. The P.E. of this 
improvement is .198, or slightly under 12 per cent of the total gain. 
The accuracy of the measurement for the 6-month schools is indi- 
cated by a P.E. showing slightly over 12 per cent of the total gain ; 
just about the same degree of reliability. 

The improvement by years varies for these schools as it does for 

TABLE IX 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 
Addition Rights in Louisville, Ky. (White Schools) 



Age 


Scores 


Total 


in 


XI 

8 
5 


X2 

16 
8 
5 


X3 

43 
16 
8 
5 




12 
10 
6 

8 


1 

16 
11 
10 
9 


2 

19 
21 
22 
19 


3 

38 
28 
23 
18 


4 

33 
31 
25 
25 


5 

27 
35 
34 
29 


6 

28 
29 
26 
26 


7 

14 

28 
28 
30 


8 

18 
27 
37 
24 


9 

10 
21 

28 
25 


10 

5 
10 
13 

18 


11 

6 
\0 
13 
13 


12 

1 
4 
6 
13 


13 

1 

2 
9 
9 


14 

3 
4 
1 


15 

1 

"2 
4 


16 

"3 
2 

2 


17 

1 
1 
1 
1 


18 


19 


20 


21 


22 


23 


X9 


289 


11 






1 










304 


1? 


1 


1 
1 


"25 


304 


13 




1 






306 














iledian 


P. E. true 
— obtained 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 

11 

12 
13 


3.77 
5.62 
6.73 
7.46 


.21 

.18 
.18 
.27 


6.26 
8.22 
9.14 
12.80 


.43 
3.17 
4.08 
5.08 


2.91 
2.52 
2.53 
3.86 


Mll-M10=1.85 
M12— Mll = l.ll 
M13— M12= .73 
M13— M10=3.69 


.170 
.155 
.202 
.213 



the 6-month schools. From ages 10 to 11 it is .18; from ages 11 to 12 
it is 1.02; and from ages 12 to 13 it is .54. The greatest gain occurs 
between the ages of 11 and 12. This occurs a year earlier than the 
greatest gain in the case of the 6-month schools. 

The median achievement for children of each age is materially higher 
than is the case in the 6-month schools. For the 13-year-old children 
this median achievement is 3.81 in the 9-month schools as against 
1.71 in the 6-month schools ; a difference of 2.10 in favor of the schools 
having the longer term. 



36 Study of Achievement in Country and Town Schools 



For the purposes of comparison, data are presented in Tables IX 
to XIII inclusive from certain other school systems. 

Table IX, for Louisville, Kentucky, is based on data in the Psycho- 
logical Laboratory of the Louisville Board of Education, and is for cer- 
tain of the white schools of the city. The tests were given under the 
direction of the Psychological Laboratory during the school year prior 
to June, 1918. 

Table X, for Louisiana, is based on tests given by the parish super- 
visors in thirteen Louisiana parishes. The schools tested were white 
schools selected by the supervisors as neither the best nor the worst 
in their respective parishes. They range in size from one teacher to 

TABLE X 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Addition Rights in Certain White Schools in Louisiana 



Age 


Scores 


Total 




XI 

24 
13 

7 


X2 

43 
24 
13 

7 


X3 

58 
43 
24 
13 




48 
47 
45 
50 


1 

31 
38 
37 
35 


2 

24 
27 
51 
42 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


X9 


XIO 


Xll 




10 
11 
12 


23 
28 
41 
31 


12 
20 
30 
98 


10 
16 
18 
16 


6 
10 
11 
16 


4 
8 
11 

8 


1 
2 
6 
6 


-.1 

1 

"5 


1 
1 
1 


1 
















287 


1 
1 










1 

1 

17 






280 








1 


1 
1 


.... 


299 


13 








277 






















Median 


P. E. true 

— obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 
11 
12 
13 


.38 
1.34 
2.46 
2.79 


.09 
.13 
.12 

.15 


2.46 
3.64 
4.20 
5.10 


0.00 
0.00 

.68 
.98 


1.23 
1.83 
1.76 
2.06 


Mil— M10= .96 
M12— Mll = 1.12 
M13— M12= .33 
M13— M10=2.41 


.094 
.106 
.114 
.102 



TABLE XI 

Age DiSTRreuTiON, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Addition Rights in Arkansas City 





Scores 


Total 




XI 


X2 


X3 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


X9 




10 


15 
8 
3 
1 


54 

15 

8 

3 


65 
54 
15 

8 


54 
49 
63 
34 


46 
33 
54 
32 


19 
35 
37 
36 


29 
17 
33 
39 


14 

29 
34 
37 


8 
10 

22 
32 


6 
4 

8 
12 


2 
3 
6 
4 










312 


11 


2 
8 
6 








259 


12 
13 


4 


3 
5 


..... 


294 
254 




Median 


P. E. true 

— obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 
11 
12 
13 


.40 
1.10 
2.10 
3.33 


.03 
.11 
.12 
.13 


1.00 
3.01 
4.22 
5.01 


0.00 

0.00 

.75 

1.64 


.50 
1.50 
1.73 
1.68 


Mil— M10= .70 
M12— Mll = 1.00 
M13-M12 = 1.23 
M13— M10 = 2.93 


.072 
.098 
.106 
.082 



sixteen teachers. In some cases only a limited number of the pupils 
were tested in each grade. When this was done, the teacher was asked 



Achievement Measured by Courtis Arithmetic Tests 



37 



to select pupils neither the brightest nor the dullest. This manifestly 
gives a selection that is not accurately representative of the Louisiana 
schools ; it seems likely that the selection tends to be above rather than 
below the median situation, and the range is less in proportion as the 
teachers and supervisors have succeeded in avoiding the extreme cases. 
Tables XI and XII, for Arkansas City and for Salina, are based on 
tabulations made from papers collected by the Bureau of Educational 
Measurements and Standards of the State Normal School at Emporia, 

TABLE XII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 
Addition Rights in Salina, Kan. 



Age 


Scores 


Total 




XI 

16 
4 
2 


X2 

20 
16 
4 

2 


X3 

43 
20 
16 

4 




46 
15 
14 
13 


1 

43 
49 
24 
13 


2 

44 
42 
38 
30 


3 

44 
36 
48 
27 


4 

26 
36 
57 
40 


5 

20 
37 
43 

32 


6 
15 

n 

29 
40 


7 

14 
8 
6 

16 


8 

12 
8 
17 


9 1 

3 

8 . 
6 
11 1 


Oil 
1 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


X9 XIO 




10 
























335 


n 


9 "i 

5 


1 
4 
4 


















2 


""2 
5 


"2 


296 


1? 


















311 


n 


1 












2 






274 


















Median 


P. E. true 

— obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 

11 

12 
13 


1.98 
3.06 
4.16 
5.25 


.12 
.13 
.12 
.15 


3.89 
5.10 
5.70 
7.25 


.10 
1.34 
2.46 
3.24 


1.89 
1.34 
1.62 
2.00 


Mil— M10=1.08 
M12— Mll = 1.10 
M13— M12 = 1.09 
M13— M10=3.27 


.120 
.114 
.114 
.120 



TABLE XIII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 
Addition Rights in Hibbing, Minn. 







Scores 










Age 












Total 




X2 
16 


X3 

34 
16 




34 
23 
11 
3 


1 

27 
30 
16 
4 


2 

31 
20 
25 

8 


3 

32 
32 
16 
15 


4 

24 

11 
10 


5 

19 
20 
19 
13 


6 

12 

12 
24 
9 


7 

12 
17 
17 
16 


8 

7 

12 
19 
18 


9 

3 
9 
16 
11 


10 

2 
9 
13 
11 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


X9 


XIO 




10 


1 
8 
4 
10 


1 
3 

7 
2 


1 
4 
3 

1 


1 
3 
3 


1 

1 
5 
2 




















257 


11 




















244 


I*? 


2 


"2 


2 
2 








2 


4 
33 


■""4 


222 


13 






1 


1 




179 














P.E. true 
















Median 


— obtained 
median 


75 per- 
centile 


25 per- 
centile 


Q 






P.E. 


10 


2.56 


.16 


4.78 


.41 


2.18 




Mil— M10=1.44 


.164 


11 


4.00 


.21 


7.22 


1.73 


2.74 




M12— Mll = 2.41 


.206 


12 


6.41 


.25 


9.34 


3.21 


3.06 




M13— M12 = 2.22 


.322 


13 


8.63 


.45 


15.12 


5.36 


4.88 




M13— M10=6.07 


.297 



38 Study of Achievement in Country and Tozvn Schools 

Kansas. The tests were given and scored by the teachers during the 
two years prior to June, 1917. 

Table XIII, for Hibbing, Minnesota, is based on papers collected by 
the Department of Research of the Hibbing schools. The tests were 
given by the teachers and scored by clerks in the fall of 1919. 

In the following summary the total improvement in ability to add 
for the three-year period from ages 10 to 13 inclusive is given for each 
system of schools reported, and also the median ability of each 13-year- 
old group. This median for the 13-year-old group may be considered 
in a way as a measure of the result obtained in any system with chil- 
dren up to the age of 13. 



School Systems 



Hibbing 

Louisville 

Salina 

Arkansas City 

Louisiana 

Madison County, 9-month schools 
Madison County. 6-month schools 



Total gain 



10 to 13 

inclusive 



Td.O? 
3.69 
3.27 
2.93 
2.41 
1.74 
1.07 



Medians 



13-year-old 
children 



8.63 
7.46 
5.25 
3.33 
2.79 
3.81 
1.71 



It is significant that the ranking in order of median ability of 13- 
year-old children so nearly coincides with ranking in order of total 
improvement for the three-year period from 10 to 13 inclusive. The 
only difference is that the order of Louisiana schools and the Madison 
County 9-month schools is inverted in the two rankings. The ability 
to add is a mechanical ability, taught definitely in the schools, and very 
little affected by the process of natural development which was so 
potent a factor in the case of language ability as measured by the Tra- 
bue Language Scale. 

Differences in method of giving the tests and in detail of procedure 
in different places affect the medians of the 13-year-old groups of chil- 
dren. These elements of error may be of determining size in cases 
where the tests are given by interested parties, such as teachers. When 
the difference between medians for groups of children of different 
ages is taken as a measure, the sources of error referred to above 
neutralize each other, since it may be assumed that the errors will be 
as great for one group of children as for another group, the tests be- 
ing given at the same time in the same system and with the same 



Achievement Measured by Courtis Arithmetic Tests 



39 



general directions or lack of directions. The ranking in order of the 
total gain in ability to add over the three-year period from ages 10 to 
13 inclusive is therefore the more significant ranking. 

The following summary shows the yearly gain in each of the sys- 
tems of schools studied : 



School Systems 



Hibbing 

Louisville 

Salina 

Arkansas City 

Louisiana 

Madison County, 9-month schools 
Madison County, 6-month schools 

Total '. 



Yearly Gains 



10 to 11 



1.44 
1.85 
1.08 
.70 
.96 
.18 
.23 



6.44 



11 to 12 



2.41 
1.11 
1.10 
1.00 
1.12 
1.02 
.13 



7.89 



12 to 13 



2.22 
.73 
1.19 
1.23 
.33 
.54 
.71 



6.95 



The extreme variation in the amount of yearly gain is significant 
in that it shows so great a lack of uniformity in the time of teaching 
so fundamental a process as that of column addition. The totals in- 
dicate that as a rule greater progress is made in teaching this process 
between the ages of 11 and 12; that the period from ages 12 to 13 is 
next; and that the least gain is made from ages 10 to 11. 



CONCLUSIONS 

1. Such difference in performance in addition as is measured by 
the Courtis Standard Research Tests can be obtained for school chil- 
dren of different ages. 

2. Since this test measures an ability trained in the schools and not 
greatly dependent on natural development, this difference in perform- 
ance is a valid measure of school efficiency in teaching this process, 

3. Material gain in ability to add may be made with children dur- 
ing any of the age periods, 10 to 11, 11 to 12, or 12 to 13. 

4. The difference in ability of children of different age-groups is a 
valid measure, even though there may have been some irregularity in 
the giving of the tests. 

5. That all the school systems investigated are doing better work in 
the teaching of addition than are the schools of Madison County. 



40 Study of Achievement in Country and Town Schools 

6. That the schools in Madison County having a 6-month school 
term are doing poorer work than the schools having a 9-month term. 
That is to say, the one- and two-teacher schools are doing poorer work 
than the larger schools. 

Section 2. Subtraction 

The data presented in subtraction are tabulated from the same sets 
of papers used for addition. The subtraction tests were given under 
the same conditions as those in addition, by the same people, and were 
corrected and collected in the same way. The statistical procedure 
has been the same in tabulating and calculating. 

Table XIV gives the facts in regard to subtraction in the Madison 
County 6-month schools. 

TABLE XIV 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Subtraction Rights in the 6-Month White Schools 

OF Madison County, Ky. 





Scores 

_ 




Age 


XI 


X2 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


X9 


XIO 


XU 


Tota 


10 
11 
12 
13 


10 
6 
3 

2 


19 
10 
6 
3 


76 
69 
61 

48 


13 
11 
13 
12 


7 
6 
13 
11 


5 
6 
10 

8 


8 
8 
8 
8 


2 
3 

7 
5 


1 

" "3 

4 




















141 


3 

4 
2 










1 


2 
4 
11 


..... 
4 


..... 


125 


2 


1 
2 






137 




1 




123 




Median 


P. E. true 

—obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 
11 
12 
13 


.54 

.67 

.97 

1.70 


.05 
.08 
.17 

.25 


1.05 
1.79 
3.67 
5.05 


.08 
.22 
.41 
.53 


.48 

.78 

1.63 

2.26 


Mil— M10= .13 

M12— Mll= .30 
M13— M12= .73 
M1.3— M10 = 1.16 


.058 
.111 
.188 
.162 



In these schools the median ability in subtraction for children 10, 
11 and 12 years of age is between and 1, and the 25 percentile for 
each of the age-groups presented falls within the same interval. Ap- 
parently most of the children in these schools under 14 years of age 
possess an ability in subtraction that is so slight that it cannot be 
measured by this test. 

The total gain in ability to subtract for the three-year period from ages 
10 to 13 inclusive, as measured by the difference between the median 
scores of the 10-year-old children and the 13-year-old children, is 1.16. 
The P.E. of this measure of gain from the true measure is .162, almost 
14 per cent of the total gain. The probable actual deviation from the 
difference obtained is reasonably small, but the very small difference 



Achievement Measured by Courtis Arithmetic Tests 



41 



obtained makes this probable deviation quite large proportionately. 
The same thing is true in the case of addition. 

The improvement from year to year increases consistently. From 
ages 10 to 11 it is .13 ; from ages 11 to 12 it is .20 ; and from ages 12 to 
13 it is .73. 

Table XV gives the facts in regard to subtraction in the Madison 
County 9-month schools. 

The median ability in subtraction of each of the age-groups is above 

1. The 25 percentiles of the 10- and 11-year-old groups fall in the 

to 1 interval. 

TABLE XV 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Subtraction Rights in the 9-Month White Schools 

OF Madison County, Ky. 









Scores 






Age 










Total 




XI 


X2 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


X9 


XIO 


Xll 




10 


9 
2 
3 


17 

9 
2 


38 
26 
25 


12 
12 
8 


6 
5 
6 


6 
6 
16 


17 
6 
10 


11 
9 
13 


7 
5 
14 


5 
6 
10 


3 
6 

7 


] 

1 


'"I 
3 


2 














124 


11 








1 
1 


'"\ 


— - 


98 


12 




1 




1 


130 


13 


4 


3 


3 


8 


13 


11 


7 


9 


.9 


6 


10 


4 


4 


i 


---- 


1 




8 


1 


1 


103 






P. E. true 














Median 


—obtained 
median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 


1.66 


.26 


4.88 


.17 


2.35 


Mil— M10= .34 


.270 


11 


2.00 


.33 


5.83 


.51 


2.66 


M12— Mll=2.50 


.280 


12 


4.50 


.31 


7.05 


1.31 


2.87 


M13— M12= .77 


.289 


13 


5.27 


.35 


8.42 


2.59 


2.91 


M13— M10=3.61 


.279 



The total gain for the three-year period from ages 10 to 13 inclusive 
is 3.61, as against a gain for a similar period of years in the 6-month 
schools of 1.16. The P.E. of the gain in the 9-month schools (3.61) 
is .279; a little less than 8 per cent of the total gain. The probable 
actual deviation of the true from the obtained difference in the case 
of the 9-month schools is greater than in the case of the 6-month 
schools, .279 as against .162, but in proportion to the respective gains 
it is less. 

The progress from year to year is uneven. From ages 10 to 11 it is 
.34; from ages 11 to 12 it is 2.50; and from ages 12 to 13 it is .77. 
By far the largest gain occurs between the ages 11 and 12. 

Tables XVI to XX inclusive present comparative data from other 
school systems, as was done for addition. In the following summary 
the total improvement in ability to subtract for the three-year period 
from ages 10 to 13 inclusive is given for each of the systems of schools 



42 Study of Achievement in Country and Toivn Schools 



TABLE XVI 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Subtraction Rights in Certain White Schools of Louisville, Ky. 





Scores 






Airp 






Total 




XI 


X2 


X3 





1 


2 


3 


4 


5 


6 


7 


8 


9 10 11 


12 


13 


14 15 16 


17 


18 


19 


20 


21 


22 


23 


24 


X9 




10 


10 


18 


45 


t; 


15 


99 


9q 


M 


'7 


97 


14 


IS 


11 


4 4 


? 


1 




1 1 




















286 


Ij 


5 


10 


18 





n 


P 


IS 


99 


'7 


•^9 


•'7 


11 


31 2inn 


1' 


3 


■i 


1 1 


1 


1 




1 




1 








313 


12 




5 


10 





(^ 


n 


1'' 


'0 


'8 


V 


"^7 


34 


23 - 


R iq 


11 


11 


in 


Q 3 


? 


5 


? 


■> 




1 








324 


13 


— - 




5 


3 


1 


1 


2 


15 


26 


20 


36 


29 


31 21 30 


16 


11 


13 


5 7 


2 


3 


2 


2 


2 






1 


26 


310 






P. E. true 














Median 


— obtained 
median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


in 


4.02 


.23 


6.42 


.10 


3.16 


Mil— M10=2.74 


.184 


11 


6.76 


.19 


9.31 


3.73 


2.79 


M12— Mll = 1.13 


.162 


n 


7.89 


.18 


10.76 


5.39 


2.68 


M13— M12 = 1.65 


.162 


13 


9.54 


.20 


12.78 


7.12 


2.83 


M13— M10=5.52 


.184 



TABLE XVII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 
Subtraction Rights in Certain Schools in Louisiana 







Scores 






Age 








Total 




XI 


X2 


X3 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


X9 


XIO 


xu 




10 
11 

n 


24 


46 


52 


5' 


'>^ 


38 


13 


I"! 


in 


W 


1 


3 


1 




















297 


14 


24 


46 


46 


35 


30 


99 


''I 


IP 


P 


f 


4 


5 


1 


1 


? 








1 






289 


7 


14 


24 


42 


23 


28 


36 


35 


29 


20 


S 


11 


9 


8 


6 






1 


1 


1 


1 




304 


13 




7 


14 


36 


18 


29 


29 


34 


21 


25 


11 


12 


12 


5 


3 


i 








16 


1 


i 


277 
















P. E. true 
















Median 


— obtained 
median 


75 per- 
centile 




25 per- 
centile 


Q 




P.E. 


10 


.31 


.13 


3.75 




0.00 


1.87 


Mil— M10=1.10 


.120 


11 


1.41 


.14 


3.98 




0.00 


1.99 


M12— Mll = 1.97 


.134 


u 


3.38 


.17 


5.65 




.73 


2.41 


M13— M12= .78 


.156 


13 


4.16 


.19 


6.79 




1.68 


2.55 


M13— M12 = 3.85 


.144 



TABLE XVIII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Subtraction Rights in Arkansas City 



Age 






Scores 




Total 




XI 


X2 


X3 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


X9 




10 


18 


5'' 


60 


37 


31 


25 


'>5 


?3 


16 


7 


8 




1 




2 










305 


11 


8 


18 


52 


33 


31 


22 


?4 


16 


18 


7 


17 


3 


1 


2 


5 










257 


12 


4 


8 


18 


29 


22 


31 


26 


45 


25 


25 


19 


16 


7 


2 


3 


2 




1 




283 


13 


1 


4 


8 


21 


10 


18 


25 


31 


20 


37 


26 


25 


11 


7 


a 


4 


2 


---- 


1 


254 






P. E. true 
















Median 


— obtained 
median 


75 per- 
centile 


25 per 
centile 




Q 




P.E. 


10 


.60 


.11 


3.23 


0.00 




1.61 


Mil— M10= .96 


.122 


11 


1.56 


.16 


4.29 


0.00 




2.14 


M12— Mll = 2.51 


.141 


17. 


4.07 


.17 


6.17 


1.53 




2.32 


M13— M12 = 1.38 


.148 


13 


5.45 


.17 


7.59 


3.06 




2.26 


M13— M10=4.85 


.130 



Achievement Measured by Courtis Arithmetic Tests 



43 



TABLE XIX 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Subtraction Rights in Salina, Kan. 



Age 






























Scores 
























Total 




XI 

15 
4 
3 


X2 

19 
15 
4 
3 


X3 

46 
19 
15 
4 




17 
11 
3 
5 


1 

21 
19 
5 
3 


2 

33 
13 
10 
4 


3 

30 
14 

27 
8 


4 

41 
40 
36 
17 


5 

35 

32 
27 
31 


6 

31 
3fi 
45 
»5 


7 

23 
23 
28 
37 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


X9 


XIO 




in 


20 
30 
33 

28 


6 
18 
27 
20 


4 
8 
19 
24 






























341 


11 


7 
11 
13 


4 

8 
6 


9 

3 

7 
























295 


1^ 


I 


3 
3 


1 

1 


1 












2 
1 


"~2 


309 


13 








2 


1 


266 
















Median 


P. E. true 

—obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 

n 

12 
13 


3.65 
5.39 
6.54 
7.35 


.19 
.19 
.16 
.15 


5.96 
7.79 
8.87 
9.72 


.30 
2.44 

4.28 
5.72 


2.83 
2.62 
2.29 
2.00 


Mil— M10=1.74 
M12— Mll = 1.15 
M13— M12= .81 
M13— M10=3.70 


.162 
.148 
.134 
.150 



TABLE XX 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Subtraction Rights in Hibbing, Minn. 







Scores 








Age 










Total 




X2 
16 


X3 

35 
16 




33 
20 
3 


1 

9 
6 

6 


2 

10 
11 


3 

12 
9 
13 


4 

14 
25 
11 


5 

22 
15 
12 


6 

20 1 
20 1 

n 1 


7 8 

6 16 

6 22 

q IS 


9 

15 
18 
IS 


10 

4 

19 
19 


11 

9 
12 

25 


12 

6 
6 
11 


13 

5 

7 

7 


14 

3 
4 
13 


1 


5 16 

. 3 
2 4 
fi 7 


17 


18 


19 


20 


21 


22 


X9 


XI 




10 




248 


11 


2 

? 


1 
3 


2 


1 










238 


12 


1 


1 


4 




227 


13 


— - 




2 


2 


4 


4 


10 


9 


3 


9 16 


13 


10 


19 


15 


5 


7 




6 1 


4 


2 




— 


1 




32 


4 


179 






P. E. true 
















Median 


— obtained 


75 per- 


25 per- 


Q 






P.E. 






median 


centile 


centile 










10 


4.64 


.30 


7.93 


.33 


3.80 




Mil— M10=2.16 


.240 


11 


6.80 


.25 


10.02 


3.72 


3.15 




M12— Mll=2.39 


.212 


12 


9.19 


.23 


11.93 


6.26 


2.83 




M13— M12=2.15 


.260 


13 


11.34 


.36 


15.87 


8.10 


3.88 




M13— M10=6.70 


.284 



reported, and also the median ability of each 13-year-old group. As 
in addition, so in subtraction, this median for the 13-year-old group 
may be considered in a v^ay as a measure of the result obtained in 
any system with children up to the age of 13. 



School Systems 



Total gain 



10 to 13 

inclusive 



Medians 



13-year-old 
children 



Hibbing 

Louisville 

Arkansas City 

Louisiana 

Salina 

Madison County, 9-month schools 
Madison County, 6-month schools 



6.70 
5.52 
4.85 
3.85 
3.70 
3.61 
1.16 



11.34 
9.54 
5.45 
4.16 
7.35 
5.27 
1.70 



44 



Study of Achievement in Country and Tozvn Schools 



The ranking in order of total gain made for the three-year period 
from ages 10 to 13 inclusive corresponds quite well with the ranking 
in order of medians for the 13-year-old children. This correspond- 
ence is not so close as was the case with addition ; there are four dis- 
placements in the ranking. As was the case with addition, the rank- 
ing in order of total gain for the three-year period is the more sig- 
nificant, since the use of a diflference as a measure tends to neutralize 
errors in the giving and scoring of the test. 

It is interesting to note that the rank in gain in ability to subtract is 
not the same as that in ability to add. Arkansas City and Louisiana 
both come ahead of Salina in subtraction, and not in addition. This 
difference between the rank of these systems for the two processes 
would seem to indicate that subtraction needs to be taught ; that im- 
provement in addition does not necessarily carry with it exactly pro- 
portionate ability to subtract. 

The following summary shows the gain for each yearly age-period 
in the systems studied : 



School Systems 


Yearly Gains 




10 to 11 


11 to 12 


12 to 13 


Hibbing- ._ .-.. 


2.21 

2.74 

.96 

1.10 

1.74 

.34 

.13 


2.34 
1.13 
2.51 
1.97 
1.15 
2.50 
.30 


2.15 


Louisville __ _- 


1.65 


Arkansas City ._ . 


1.38 


Louisiana ..- 


.78 


Salina . . . 


.81 


Madison County, 9-month schools . 


.77 


Madison County, 6-month schools . - _ - 


.73 






Total 


9.22 


11.90 


8.27 







The variations are as great in the amount of yearly gain as they 
were shown to be in addition. As in addition, so in subtraction, the 
greatest yearly gain seems to be between the ages of 11 and 12. In 
subtraction the next greatest gain seems to be between the ages of 10 
and 11, while in the case of addition the second greatest gain was be- 
tween the ages of 12 and 13. The smallest gain is made between the 
ages of 12 and 13. 

CONCLUSIONS 

1. The conclusions reached in regard to addition (p. 39) hold in the 
case of subtraction. 



Achievement Measured by Courtis Arithmetic Tests 



45 



2. Improvement in addition does not necessarily carry with it pro- 
portionate ability to subtract. 

Section 3. Multiplication 

The data presented in multiplication are from the same sources as 
those for addition and subtraction, and the method of treatment has 
been the same throughout. 

Table XXI gives the facts in regard to multiplication in the Madison 
County 6-month schools. 

TABLE XXI 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Multiplication Rights in the 6-Month White Schools 

OF Madison County, Ky. 





Scores 




Age 




Total 




XI 


X2 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


X9 


XIO 


Xll 




in 


9 

8 
4 
2 


19 
9 
6 

4 


82 
75 
62 
57 


16 
11 
12 
15 


3 
11 

16 

8 


5 
8 
12 
9 


4 
2 

9 
5 


1 
2 
3 
3 


1 


























140 


11 




















2 
4 
10 


"""2 
4 


.... 


124 


1? 


4 


1 

1 
















1 


136 


18 


4 














124 
























P. E. true 














Median 


—obtained 


75 per- 


25 per- 


Q 




P.E. 






median 


centile 


centile 








10 


.51 


.04 


.93 


.08 


.42 


Mil— M10=.ll 


.036 


11 


.62 


.05 


1.27 


.21 


.53 


M12— Mll = .31 


.094 


12 


.93 


.14 


3.16 


.38 


1.39 


M13— M12 = .05 


.142 


13 


.98 


.18 


3.77 


.43 


1.67 


M13— M10 = .47 


.111 



The median of each of the age-groups given falls below 1, and even 
the 75 percentile of the 10-year-old group falls between and 1. It 
seems that most of the children in these schools below the age of 14 
have an ability in multiplication that is less than can be measured by 
the Courtis Standard Research Tests in Arithmetic Series B. 

The total gain in ability to multiply during the three-year period, ages 
10 to 13 inclusive, is only .47. The P.E. of this statement of gain is 
.111, something over 25 per cent of the gain itself. The gain noted is 
very slight. Apparently these 6-month schools in Madison County are 
failing to teach most of the pupils under 14 how to multiply. 

The improvement from year to year necessarily is very slight, since 
the total improvement is so small. From ages 10 to 11 the improve- 
ment is .11 ; from ages 11 to 12 it is .31 ; and from ages 12 to 13 it is 
.05. The greatest gain in any one-year period is .31 from ages 11 to 12. 

The results of instruction in multiplication in these schools are very 
meager. 



46 



Study of Achievement in Country and Town Schools 



TABLE XXII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Multiplication Rights in the 9-Month White Schools 

OF Madison County, Ky. 







Scores 






Asje 








Total 




XI 


X2 





1 


2 


3 4 


5 


6 


7 


8 


9 


10 


11 


X9 


XIO 


Xll 




10 


9 

1 
3 


16 
9 

1 


37 
31 

32 


4 

10 
14 


12 
7 
14 


14 10 

7 12 

23 16 


12 
11 
10 


6 
4 



















120 


11 






3 


'"2 


— - 


1 
1 






96 


12 


3 


2 


i 




131 


18 


4 


3 


13 


10 


11 




1 9 


12 


11 


5 








2 


8 


1 


1 


101 
















P. E. true 
















Median 


— obtained 
median 


75 per- 
centile 


25 per- 
centile 


Q 






P.E. 


10 


.94 


.21 


3.85 


.13 


1.86 


Mil— M10= 


.76 


.206 


11 


1.70 


.26 


4.58 


.45 


2.06 


M12-M11 = 


1.36 


.200 


12 


3.06 


.20 


4.56 


.87 


1.84 


M13— M12 = 


.80 


.216 


13 


3.86 


.29 


6.25 


1.52 


2.36 


M13— M10= 


2.92 


.222 



Table XXII gives the facts in regard to multiplication in the 9- 
month schools of Madison County. 

The median ability in multiplication in these schools for 10-year-old 
children is .94; a Httle less than 1. The 25 percentile of the 10-, 11- 
and 12-year-old groups is less than 1 in each case. The situation 
here presented is materially better than that in the 6-month schools. 

The total gain in ability to multiply for the three-year period from ages 
10 to 13 inclusive is 2.92. The contrast between this gain and that in 
the 6-month schools (.47) is marked. The P.E. of this gain of 2.92 
is .222, a little over 7 per cent of the gain. The probable actual de- 
viation of the true from the obtained measure is greater in the case of 
the 9-month schools than in the case of the 6-montli schools, but in 
proportion to the gain made it is much less. 

The improvement in ability to multiply from ages 10 to 11 is .76; 
from ages 11 to 12 it is 1.36; and from ages 12 to 13 it is .80. The 
gain during any one of the year periods is much greater than the gain 
for the entire three-year period in the 6-month schools. The great- 
est gain is from ages 11 to 12, as is the case in the 6-month schools. 

Tables XXIII to XXVII inclusive give comparative data in regard 
to multiplication from other school systems. In the following sum- 
mary the total improvement in ability to multiply during the three-year 
period from ages 10 to 13 inclusive is given for each of the school sys- 
tems studied, and also the median ability for the respective groups of 
13-year-old children. The schools are listed in the order of amount of 
improvement made. 



Achievement Measured by Courtis Arithmetic Tests 



47 



TABLE XXIII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Multiplication Rights in Certain White Schools in Louisville, Ky. 



Age 


Scores 


Total 


XI 

10 
5 


X2 

10 
5 


X3 

43 
16 
10 

5 




7 

10 
2 
3 


1 

15 

8 
9 
3 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 




10 
11 
12 
13 


23 
11 
U 
9 


34 
17 
18 
18 


32 
37 
31 
22 


30 
41 
34 
32 


26 
36 
38 
43 


21 
35 
35 
40 


12 
32 
41 
38 


5 
21 
34 
34 


7 
14 
15 
18 


3 
3 
17 
13 














284 


7 
9 
13 


5 
6 

8 


1 

2 
2 








309 


""■4 


2 


1 


320 
305 










Median 


P. E. true 

— obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 
11 

12 
13 


3.82 
5.98 
7.05 
7.43 


.21 
.14 
.15 
.14 


6.11 

8.17 
9.17 
9.46 


.28 
4.00 
4.80 
5.50 


2.91 
2.08 
2.18 
1.98 


Mil— M10 = 2.16 
M12— Mll = 1.07 
M13— M12= .38 
M13— M10=3.61 


.158 
.127 
.120 
.152 



TABLE XXIV 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Multiplication Rights in Certain White Schools in Louisiana 



Age 


Scores 


Total 


XI 

24 
13 

7 


X2 

42 
24 
13 

7 


X3 

61 
43 
24 
13 




69 
63 

74 
50 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


X9 


XIO 


Xll 




10 
11 
12 
13 


24 
31 
36 
33 


21 
30 

28 
35 


21 
26 
34 
25 


12 
16 
34 

27 


8 
11 
21 
23 


4 
9 
12 
17 


2 
7 
5 
16 


















289 


4 
6 
3 


1 
3 
2 


'"3 




1 

1 

1 1 


1 

1 

17 






280 


1 

1 




300 


1 


275 




Median 


P. E. true 

— obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 
11 
12 
13 


.23 

.95 

1.88 

2.98 


.06 
.12 
.13 
.17 


1.85 
3.23 
4.26 
5.70 


0.00 

0.00 

.41 

.97 


.92 
1.61 
1.92 
2.86 


Mil— M10= .72 
M12-M11= .93 
M13— M12 = 1.10 
M13— M10=2.75 


.080 
.106 
.136 
.117 



TABLE XXV 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Multiplication Rights in Arkansas City 



Age 


Scores 


Total 


XI 


X2 


X3 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


X9 




10 
11 
12 
13 


14 

8 
4 
1 


51 
14 

8 
4 


61 
51 
14 

8 


63 
41 
49 
30 


44 
21 
25 
13 


24 
40 
38 
22 


24 
22 
50 
24 


11 
21 
31 
3C 


6 
15 

22 
22 
















298 


9 
28 
28 


6 
16 
16 


2 

2 

24 


8 
4 
4 










258 


2 
3 


1 
6 


2 
4 


. 


296 
245 




Median 


P. E. true 

— obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 
11 
12 
13 


.36 
1.71 
3.20 
4.51 


.06 
.14 
.15 
.19 


1.78 
3.84 
5.13 
6.88 


0.00 

0.00 

.97 

2.01 


.89 
1.92 
2.08 
2.43 


Mil— M10=1.35 
M12— Mll = 1.49 
M13— M12 = 1.31 
M13— M10=4.15 


.098 
.127 
.150 
.126 



48 Study of Achievement in Country and Town Schools 

TABLE XXVI 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Multiplication Rights in Salina, Kan. 





Scores 




Age 




Total 




XI 


X2 


X3 





1 


2 


3 


4 


5 


6 


7 


8 


9 10 11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


X9 


XIO. 




10 


16 
3 
3 


22 

16 

3 

1 


48 
22 
16 
3 


31 
19 

8 
6 


27 
17 
8 
8 


20 
22 
11 
13 


23 
23 
29 
11 


18 
21 
29 
31 


48 
52 
45 

27 


24 
22 
.51 
46 


10 

8 
19 
29 


9 
10 
33 

28 


4 
17 
27 1 
19 1 


4 




























334 


11 


i 5 
9 19 
15 


2 
3 

7 


"7 
4 


2 
1 

8 


1 


1 


















267 


1? 














2 
4 


"i 


333 


13 


- 


— 


2 










2 


275 


















P. E. true 














Median 


— obtained 
median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 


3.13 


.18 


5.32 


0.00 


2.66 


Mil— M10=1.41 


.155 


11 


4.54 


.18 


6.23 


1.39 


2.44 


M12-M11 = 1.64 


.148 


12 


6.28 


.16 


8.84 


4.18 


2.33 


M13— M12= .53 


.156 


13 


6.81 


.20 


9.18 


4.86 


2.66 


M13— M10 = 3.68 


.162 



TABLE XXVII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Multiplication Rights in Hibbing, Minn. 







Scores 




Age 






Total 




X2 
18 


X3 

35 
16 




34 
19 


1 

23 
11 

in 


2 

29 

24 
1? 


3 

35 
25 
17 


4 

20 
23 
27 


5 

21 

42 
29 


6 

16 

25 

27 


7 

12 
19 

26 


8 

9 
10 
18 


9 

5 
15 
18 


10 

4 
8 
10 


11 

1 
1 
3 


12 

1 
2 
9 


13 


14 


15 


16 


17 


X9 


no 




in 


261 


11 


2 
6 


1 
1 


"4 


1 
1 








244 


12 


1 


4 




230 


13 






3 


6 


4 


12 


12 


13 


13 


17 


16 


11 


12 


12 


8 


3 




2 






33 


4 


181 


















p. E. true 
















Median 


—obtained 
median 




75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 


2.77 


.18 




5.17 


.41 


2.38 


Mil— M10=2.32 


.140 


11 


5.09 


.17 




6.92 


2.62 


2.15 


M12— Mll = 1.39 


.140 


12 


6.48 


.18 




8.97 


4.42 


2.27 


M13— M12 = 2.17 


.220 


13 


8.65 


.32 




12.59 


5.63 


3.48 


M13— M10=5.88 


.220 



As is the case in addition and subtraction, the ranking in order of 
gain made in abiHty for the three-year period from ages 10 to 13 inclu- 
sive does not correspond exactly with the ranking in order of ability of 



School Systems 



Hibbing 

Arkansas City 

Salina 

Louisville 

Madison County, 9-month schools. 
Louisiana 

Madison County, 6-month schools. 



Total gain 


Medians 


10 to 13 


13-year-old 


inclusive 


children 


5.88 


8.65 


4.15 


4.51 


3.68 


6.81 


3.61 


7.43 


2.92 


3.86 


2.75 


2.98 


.47 


.98 



Achievement Measured by Courtis Arithmetic Tests 



49 



13-year-old children. The measure of gain made is probably the 
more significant measure, as for addition and subtraction. 

It must be borne in mind that the steps of improvement are not 
necessarily of equal value. It may be more difficult to teach a child 
who cannot multiply to multiply well enough to do one example cor- 
rectly than it is to teach a child who can do one example correctly to do 
two examples correctly. In other words, because Hibbing makes twice 
as much improvement as Louisiana does not necessarily mean that the 
teaching in Hibbing is twice as good as that in Louisiana. This dif- 
ficulty in evaluating the results of this test is not due to the fact that 
a difference between the median abilities of age-groups is used as a 
measure, but rather to the manner in which the test is constructed. 
The unit in which the result is stated is not one of the relative diffi- 
culty with which those results are obtained. 

The following summary shows the gain for each yearly age period 
in the systems studied: 



School Systems 




Yearly Gains 




10 to 11 


11 to 12 


12 to 13 


Hibbing. . _.._. . 


2.32 

1.35 

1.41 

2.16 

.76 

.72 

.11 


1.39 
1.49 
1.64 
1.07 
1.36 
.93 
.31 


2.17 


Arkansas City _. . _ . .. 


1.31 


Salina 


.53 


Louisville- ._.--_ 


.38 


Madison County, 9-month schools 


.80 


Louisiana .. - . _ .. 


1.10 


Madison County, 6-month schools. . 


.05 






Total 


8.83 


8.19 


6.34 



The variations in amount of yearly gain are as great as they are in 
addition and subtraction. The greatest gain seems to be between 
ages 10 and 11 in this case, while in both addition and subtraction the 
greatest gain seems to come between ages 11 and 12. The smallest 
gain appears between ages 12 and 13. 

The conclusions in regard to multiplication are the same as those for 
addition (p. 38) and subtraction (p. 44). 



Section 4. Division 
The data presented in division are from the same sources as those 
for addition, subtraction and multiplication, and the same method of 
treatment has been followed. 



50 Study of Achievement in Country and Tozvn Schools 

Table XXVIII gives the facts in regard to division in the 6-month 
schools of Madison County. 

TABLE XXVIII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 
Division Rights in the 6-Month White Schools of Madison County, Ky. 













Scores 








Age 
















Total 




XI 


X2 





1 


2 


3 


4 


5 


6 


7 


8 


X9 


XIO 


Xll 




in 


10 

6 


17 
10 


98 
83 


7 
15 




4 

1 


1 

5 




2 
2 
















139 


n 


1 




1 




2 






126 


12 


3 


6 


78 


16 




9 


7 




6 


4 


1 






4 


2 




138 


1'^ 


2 


3 


70 


16 




8 


5 




1 




1 






11 


4 


2 


123 














P. E. true 


















Median 


— obtained 
median 




75 per- 
centile 




25 per- 
centile 


Q 




P.E. 


10 


.43 


.03 




.78 




0.07 


.35 


Mil— M10= .13 


.028 


11 


.56 


.04 




.94 




.18 


.38 


M12— Mll= .20 


.053 


12 


.76 


.09 




2.05 




.32 


.86 


M13-M12= .04 


.078 


13 


.80 


.10 




2.15 




.36 


.89 


M13-M10= .37 


.072 



In these schools the median ability in division of each of the age- 
groups from ages 10 to 13 inclusive is between and 1. For the ages 10 
and 11 the 75 percentiles are in the same interval. It seems that in 
division, as in multiplication, the majority of the children under 14 
years of age in the Madison County 6-month schools are unable to 
work correctly any of the examples given in the Courtis Standard 
Research Tests in Arithmetic Series B for division. 

The total gain in ability to divide during the three-year period from 
ages 10 to 13 inclusive is from .43, the median for the 10-year-old chil- 
dren, to .80, the median for the 13-year-old children, a difference of .37. 
The P.E. of this difference is .072 — about 20 per cent of the gain. 
This gain is very small for so long a period of time at the age when 
material progress is being made in this ability in other school systems. 

As would be expected where the total improvement is so small, the 
yearly gains are very small and uneven. From ages 10 to 11 the gain 
is .13; from ages 11 to 12 it is .20; and from ages 12 to 13 it is .04. 
The P.E. of the gain from ages 12 to 13 is .072, which is almost twice 
as much as the gain. This means that the gain in this year is almost 
negligible. 

Table XXIX gives the facts in regard to division in the Madison 
County 9-month schools. 



Achievement Measured by Courtis Arithmetic Tests 



51 



TABLE XXIX 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 
Division Rights in the 9-Month White Schools of Madison County, Ky. 



Age 


Scores 


Total 




XI 


X2 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


X9 


XIO 


Xll 




10 


9 

1 
3 
5 


16 
9 
1 
3 


60 

46 
45 
17 


5 
6 
13 
15 


8 
11 
9 

8 


5 
3 
10 
11 


9 

7 
13 

7 


4 
2 
11 
6 


3 

2 
8 
6 


1 

2 
8 
3 


1 
4 

2 
3 


1 
1 
1 
3 


1 
1 
1 

1 




1 










124 


11 




1 
1 

8 






96 


12 


2 


— 


.... 


1 

1 




129 


13 


1 


99 












Media 


n 


P. E. true 

— obtained 

median 


75 per- 
centile 


1 

j 25 per 

! centile 




Q 




P.E. 


10 
11 
12 
13 


.61 

.82 

2.27 

3.13 


.12 
.16 
.21 
.33 


2.37 
2.90 
5.31 
6.37 


.11 

.30 
.63 
.98 


1.13 
1.30 
2.34 
2.69 


Mll-M10= .21 
M12— Mll = 1.45 
M13— M12= .86 
M13— M10=2.52 


.122 
.190 
.264 
.210 



In these schools the 25 percentile of each of the age-groups from ages 
10 to 13 inclusive falls between and 1, and the medians for the 10- 
and 11-year-old groups each fall in the same interval. A much larger 
proportion of the children reported are able to work some of the ex- 
amples correctly than is the case in the 6-month schools. 

The total gain from ages 10 to 13 inclusive in this case is 2.52 as 
against .37 in the case of the 6-month schools in the same county. The 
P.E. of the gain for the 9-month schools is .21, about 8.5 per cent of the 
gain. The probable actual deviation of the true measure of gain from 
the measure of gain given is almost three times as great as the like 
probable deviation in the case of the 6-month schools, but the gain in 
the case of the 9-month schools is so much greater that proportion- 
ately the probable deviation is smaller. 

As in the 6-month schools, so in these, the yearly gains are unequal. 
From ages 10 to 11 the gain is .21 ; from ages 11 to 12 it is 1.45 ; and 
from ages 12 to 13 it is .86. The gain for each year after the first is 
much greater than the total gain in the 6-month schools for the entire 
three-year period. 

Tables XXX to XXXIV inclusive give comparative data from other 
school systems in regard to division. In the following summary the 
total gain in ability to divide during the three-year period from ages 10 
to 13 inclusive is given for each of the systems studied, and also the 
median abihty of the 13-year-old children in the respective systems. 
The schools are listed in the order of the amount of improvement 
made. 

In this table it is interesting to note that the ranking in order of 
amount of total gain corresponds exactly to ranking in order of the 



52 Study of Achievement in Country and Town Schools 



TABLE XXX 

Age Distribution, 10 to 13 Inclusi\'e, of Courtis Series B Arithmetic Tests 
Division Rights in Certain White Schools of Louisville, Ky. 





Scores 




Age 




Total 




XI 

10 
5 


X2 

16 
10 
5 


X3 

43 3 
16 2 
10 1 
5 1 


1 

24 
3 12 
6 12 

1 9 


2 

31 
16 
15 
13 


3 

24 
23 
18 
16 


4 

32 
28 
22 
13 


5 

21 
25 

22 
21 


6 

20 

22 
23 
34 


7 

13 
20 
27 
23 


8 

9 
18 
27 
30 


9 

11 
19 

23 
25 


10 

3 
21 

23 
26 


U 

3 

12 
10 

25 


12 

4 
12 
17 
18 


13 

2 
9 
11 
13 


14 1 

7 
12 
6 1 


5 16 


17 


18 


19 20 


21 


22 


23 


24 


X9 




10 






















297 


11 


3 3 

i 3 
2 6 


2 
6 
2 


1 
4 












1 
1 


""26 


308 


12 


] 








319 


13 


) 








336 




















P. E. true 














Median 


— obtained 
median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 


2.82 


.19 


5.60 


.17 


2.71 


Mil— M10 = 3.02 


.192 


11 


5.84 


.24 


9.68 


2.68 


3.50 


M12— Mn = 1.77 


.204 


12 


7.61 


.23 


10.83 


4.17 


3.33 


M13— M12 = 1.15 


.191 


13 


8.76 


.21 


12.05 


5.80 


3.12 


M13— M10=5.94 


.176 



TABLE XXXI 
Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 







Division Rights 


IN 


Certain White Schools 


IN 


Louisiana 








Scores 






Age 






Total 




XI 


X2 


X3 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


X9 


XIO 


XI 1 




in 


24 
14 

7 


43 
24 
14 


59 

43 
24 


106 
90 
103 


16 

27 
32 


17 
19 
31 


9 
16 

22 


4 
16 
23 


4 
9 
13 


2 
7 
8 


'"h 

7 


1 
3 

8 


1 

3 

7 


















286 


11 


1 

1 


2 






2 
1 


1 
1 






282 


12 


1 


1 


1 




305 


13 


.... 


7 


14 


75 


37 


18 


15 


26 


22 


13 


10 


12 


6 


4 


3 




1 




16 


1 


1 


281 






P. E. true 














Median 


— obtained 
median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 


.16 


.02 


.83 


0.00 


.33 


Mil— M10= .50 


.060 


11 


.66 


.09 


2.70 


0.00 


1.35 


M12— Mll= .48 


.092 


12 


1.14 


.12 


3.80 


.30 


1.75 


M13— M12=1.27 


.138 


13 


2.41 


.19 


5.85 


.65 


2.60 


M13— M10=2.25 


.120 



TABLE XXXII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Division Rights in Arkansas City 







Scores 








Age 










Total 




XI 


X2 


X3 





1 


3 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


X9 




in 


16 

8 


49 
16 


60 
49 


86 
81 


43 
38 


22 
10 


1 


9 7 
6 9 


2 
9 


"'6 


"5 


- 


7 


1 
1 
















295 


11 


2 














257 


n 


4 


8 


16 


82 


45 


37 


1 


9 19 


11 


15 


1? 




6 


in 


q 






1 








294 


13 


1 


4 


8 


42 


29 


25 


2 


3 19 


25 


23 


15 




5 


8 


10 


5 


1 


3 


— - 


1 


1 


248 






P. E. true 
















Median 


— obtained 
median 


75 per- 
centile 


25 per- 
centile 




Q 




P.E. 


10 


.26 


.04 


1.23 


0.00 




.61 


Mil— M10= .42 


.053 


11 


.68 


.08 


2.07 


0.00 




1.03 


M12— Mll = 1.14 


.102 


12 


1.82 


.14 


4.50 


.55 




1.97 


M13— M12=1.83 


.150 


13 


3.85 


.20 


6.43 


1.24 




2.59 


M13— M10=3.39 


.121 



Achievement Measured by Courtis Arithmetic Tests 53 



TABLE XXXIII 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Division Rights in Salina, Kan. 



ARe 


Scores 


Total 

335 
297 


10 
11 


XI 

16 
3 
3 


X2 

21 
16 
3 
3 


X3 

47 
21 
16 
3 




48 
36 
22 
11 


1 

41 
21 
18 
17 


2 

39 
29 
28 
20 


3 

27 
37 
25 

27 


4 

28 
17 
32 
25 


5 

21 
29 
33 
29 


6 

21 
16 
29 
31 


7 

9 
16 
25 
14 


8 

12 
25 

28 
20 


9 10 11 

2 .. 2 
7 5 4 
9 21 8 
11 18 14 


12 

1 
4 
10 

8 


13 

5 
5 
10 


14 15 16 

2 V. "2 
2 1 2 
2 ._ 2 


17 


18 


19 


20 


21 


22 
"2 


23 


24 
"2 


X9 


XIO 


12 
13 


2 
5 


""2 


322 
275 




Median 


P. E. true 

— obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 
11 
12 
13 


1.86 
3.60 
5.45 
6.80 


.15 
.21 
.19 

.22 


4.43 
6.85 
8.26 
9.56 


0.00 

.95 

2.86 

3.54 


2.21 
2.95 

2.80 
3.01 


Mil— M10= 1.74 
M12— Mll = 1.85 
M13— M12 = 1.35 
M13— M10=1.96 


.158 
.176 
.176 
.166 



TABLE XXXIV 

Age Distribution, 10 to 13 Inclusive, of Courtis Series B Arithmetic Tests 

Division Rights in Hibbing, Minn. 



Age 


Scores 


Total 




X2 


X3 





1 


2 


3 


4 


5 


6 


7 8 


9 


10 


11 I 


2 13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


X9 


XIO 




10 


16 


35 
16 


98 
60 
28 
14 


11 
22 
10 
10 


14 
21 
20 
4 


11 
16 
12 
4 


17 
13 
26 
11 


11 
15 
19 

8 


12 1 

13 1 
18 1 

9 1 


1 4 
3 11 
3 14 
3 12 


4 
10 
16 

9 


5 
12 
13 
10 


1 
7 

4 1 

5 1 


5 2 
9 1 
3 3 

8 


i 

3 
6 


1 

'5 

2 


— 


~" 


— 


— 


— 


— 


— 


— 


— 








258 


11 


1 
3 


1 


"2 
2 


1 

"i 
















243 


1' 


2 


1 


1 

1 




1 


4 
32 


"1 


229 
178 


13 














Median 


P. E. true 

—obtained 

median 


75 per- 
centile 


25 per- 
centile 


Q 




P.E. 


10 
11 
12 
13 


.79 
3.15 
5.97 
9.44 


.17 
.27 
.27 
.45 


4.50 

7.48 

9.73 

15.12 


.13 

.74 

2.96 

5.18 


2.18 
3.37 
3.38 
4.92 


Mil— M10=2.36 

M12— Mll=2.82 
M13— M12 = 3.47 
M13— M10=8.65 


.172 
.220 
.327 
.172 



size of the median for the 13-year-old children. This is not true in 
the case of addition, subtraction, or multiplication, though in each case 
there is a marked similarity in the ranking. 



School Systems 



Total gain 



10 to 13 
inclusive 



Medians 



13-year-old 
children 



Hibbing 

Louisville 

Salina 

Arkansas City 

Madison County, 9-month schools 
Louisiana 

Madison County, 6-month schools 



8.65 
5.94 
4.96 
3.39 
2.52 
2.25 
.37 



9.44 
8.76 
6.80 
3.65 
3.13 
2.41 
.80 



CHAPTER V 

ACHIEVEMENT AS MEASURED BY THE THORNDIKE SILENT 
READING SCALE ALPHA 2 



The Thomdike Silent Reading Scale Alpha 2 was used to measure 
reading in the schools of Madison County at the same time that the 
tests were given in Language and Arithmetic. This scale is designed 
to be used as a group test, and the directions for scoring are given on 
the basis of groups of pupils such as would be found in one room of a 
city school system. In country schools such groups do not exist, and 
therefore individual scores were assigned each pupil, on the basis of 
tables prepared by Dr. Truman Lee Kelley.^ 

Using the individual scores assigned on the basis of these tables, the 
remaining problems involved in finding the differences in performance 
in reading of different age-groups are practically the same as in the 
work with the Trabue Language Scale and the Courtis Standard Re- 
search Tests in Arithmetic. Distributions for the respective age- 
groups are completed on the same assumptions, and the same age- 
groups are used throughout. Scores used are in terms of difficulty as 
assigned by Thorndike. 

Table XXXV gives the facts in regard to reading in the Madison 
County 6-month schools. The table reads, there are estimated to be 
8 children 10 years old in the first grade (XI) whose scores in read- 
ing are unknown, 10 children 10 years of age with scores unknown 
are estimated to be in the second grade (X2), 1 child 10 years old 
made a score of 2.0, 5 made a score of 2.2, 3 a score of 2.6, 3 a score 
of 2.9, 2 a score of 3.2, etc. 

The total gain in ability to read for the three-year period from ages 
10 to 13 inclusive is from 4.50 to 5.26, a difference of .76. The P.E. of 
this difference is .09, or about 12 per cent of the total. This gain is 
very small for a three-year period, and the P.E. of the gain is relatively 
quite large. 

The improvement from year to year is very uneven. From ages 10 
to 11 it is .03 ; from ages 11 to 12 it is .59; and from ages 12 to 13 it is 
.14. The results indicate rather indefinite work in reading. 



^ Kelley, T. L. : "Thorndike's Reading Scale Alpha 2 Adapted to Individual 
Testing," Teachers College Record, XVIII: 253#. (May, 1917). 

56 



TABLE XXXV 
Age Distribution, 10 to 13 Inclusive, of Thorndike Silent Reading Scale Alpha 2 Scores in the 6-Month White Schools of Madison County, Ky. 







Scores 




Age 










XI 


X2 


2.0 


2.1 


2.2 


2.3 


2.4 


2.5 


2.6 


2.7 


2.8 


2.9 


3.0 


3.1 


3.2 


3.3 


3.4 


3.5 


3.6 


3.7 


3.8 


3.9 


4.0 


4.1 


4.2 


4.3 


4.4 


4.5 


4.6 


4.7 


4.8 


4.9 


5.0 


5.1 


5.2 


5.3 


5.4 


5.5 


5.6 


5.7 


5.8 


5.9 


6.0 


6.1 0.2 


6.3 


6.4 


6.5 


6.6 


6.7 


6.8 


6.9 


7.0 


7.1 


7.2 


7.3 


7.4 


7,, 5 


7.6 


7.7 


X9 


XIO 


XII 


10 


8 


10 


1 


_._ 


5 


-.- 


.._ 




3 




... 


3 






2 


6 






4 


1 






1 


12 


1 


2 


2 


11 






2 


18 


3 


5 


4 


1 




? 


? 


? 


4 




•-> 


" 






— 






— 


— 


— 


— 


— 


— 


— 


— 


— 


— 


— 


— 


— 




11 
12 


4 
3 


8 
4 






4 

2 








2 


i 


... 


4 

1 




2 


4 

1 


5 
6 






6 
4 


1 
4 






1 
1 


5 
6 


... 


5 

1 


... 


9 

in 




1 

1 


2 
3 


9 

in 


1 

5 


5 
10 


7 
8 


1 


1 

9 


] 


2 

9 


'3 


■^ 


1 


3 
4 
2 




3 
4 

7 




2 
2 
2 


4 

2 


1 

7 
7 


""2 

1 


"'3 


"I 


' i 














— 


"'2 


— 


— 


13 


1 


3 


z. 


z. 


1 






z. 


i 


i: 




2 


i: 


2 


:i 


1 




Z 


2 










5 




2 


1 


9 


... 




7 


10 


1 


8 


4 


2 


3 


1 


2 




4 




2 


1 




"i 


1 


::: 








'" 


"i 


1 


3" 


"1 










P. E. true 

















Age 


Total 


Median 


— obtained 


75 per- 


25 per- 


Q 






P E 










median 


centile 


centile 














10 


122 


4.50 


.10 


5.01 


3.22 


.89 




Mil— M10= .03 


.09 




11 


107 


4.53 


.12 


5.23 


3.24 


.99 




M12— Mll= .59 


.09 




12 


131 


5.12 


.09 


6.06 


4.37 


.84 




M13— M12= .14 


.09 


































13 


117 


5.26 


.11 


6.59 


4.59 


1.00 




M13— M10= .76 


.09 



































TABLE XXXVI 
Age Distribution, 10 to 13 Inclusive, of Thorndike Silent Reading Scale Alpha 2 Scores in the 9-Month White Schools of Madison County, Ky. 



Afp 






Scores 




10 


XI 

6 

'"'3 
3 


X2 

13 
6 





2.2 

2 

1 


2.3 


2.4 


2.5 


2.6 

1 
1 


2.7 

1 


2.8 


2.9 

5 
1 
3 


3.0 

"i 


3.1 


3.2 

2 
2 


3.3 

5 

2 
3 


3.4 
"i 


3.5 

1 
1 
2 


3.6 

5 
2 
2 


3.7 

"2 


3.8 


3.9 


4.0 

2 

1 


4.1 

4 
5 
2 
1 


4.2 


4.3 

4 
1 
2 


4.4 
"I 


1.5 

7 
5 
3 

2 


4.6 


1.7 
2 

"i 


4.8 

3 

1 
2 
3 


4.9 

2 
3 
5 

2 


5.0 
5 

"3 

2 


5.1 

' 8 

"i 

2 


5.2 

3 
3 
4 

2 


5.3 
"2 


5.4 

"2 

1 


5.5 

5 
5 
3 

4 


5.6 

2 
2 
2 


5.7 

1 

2 
4 

2 


5.8 

1 
1 

4 
3 


5.9 

1 
2 
1 
1 


6.0 

3 
4 
6 
3 


6.1 

"i 

1 


6.2 

1 
4 
6 
3 


6.3 

"2 
3 


6.4 

1 

""i 

1 


6.5 

1 
2 
3 

8 


6.6 

3 
4 
9 
3 


6.7 

3 

1 
5 

7 


6.8 
2 

"3 

2 


6.9 

"i 

"3 


7.0 

1 
2 
1 
3 


7.1 

1 
2 
1 
1 


7.2 

i 
3 
1 


7.3 

1 
2 
2 


7.4 


7.5 


7.6 


7.7 


7.8 


7.9 


8.0 


8.1 


8.2 


8.3 


8.4 


8.5 


8.6 


8.7 

1 


X9 


XlO 


xu 


11 






1 




























2 

1 
7 


""2 
I 




1? 


1 

1 




1 




1 




1 


















13 


3 










1 












2 


















9 

















































































P. E. true 














Age 


Total 


Median 


—obtained 
median 


75 per- 
centile 


25 per- 
centile 


Q 






P. E. 


10 


109 


4.55 


.15 


5.51 


2.98 


1.26 


Mil— M10= 


.75 


.14 


11 


84 


5.30 


.17 


6.25 


3.75 


1.25 


M12— Mll = 


.66 


.13 


12 


107 


5.86 


.10 


6.65 


4.95 


.85 


M13— M12 = 


.59 


.10 


13 


83 


6.45 


.13 


7.01 


5.14 


.93 


M13— M10=l 


.90 


.12 



Achievement Measured by Thorndike Reading Scale 57 

Table XXXVI gives the facts in regard to reading in the 9-month 
schools of Madison County. 

The total gain for the three-year period in this case is from 4.55, 
the median ability of the 10-year-old children, to 6.45, the median 
ability of the 13-year-old children, a difference of 1.90. This gain is 
just 2.5 times as great as that made in the 6-month schools of the 
same county. The median abilities of the 10-year-old children are 
about alike. The comparison of amount of gain in the two cases is 
valid, since the scores given are in terms of difficulty for the children. 
It must be remembered, however, that there is no proof that the gain 
in each case can be attributed solely to school work. It is possible 
that influences outside of the school contribute materially to the re- 
sult. The conclusion can only be that school influence on reading and 
other possible influence on reading accomplish between them 2.5 times 
as much in places having a 9-month school term as do the same in- 
fluences in places having a 6-month school term. 

The P.E. of the gain in the 9-month schools (1.90) is .12, about 
7 per cent of the gain. The probable actual deviation of the true dif- 
ference from the obtained difference in these schools is a little larger 
than the like deviation in the 6-month schools, but in proportion to the 
gains made in the respective schools the deviation is less in the 9-month 
schools. 

The yearly gains are much more nearly uniform than in the 6-month 
schools. From ages 10 to 11 the gain is .75 ; from ages 11 to 12 it is 
.56; and from ages 12 to 13 it is .59. 

Tables XXXVII to XXXIX inclusive give comparative data in re- 
gard to reading from certain other school systems. The data from 
Louisville are based upon tests given by the Psychological Laboratory 
of the Louisville Board of Education. Data for Hamilton Town- 
ship, New Jersey, were collected by the Psychology Department of 
the Trenton State Normal School. The data from Amsterdam, New 
York, were collected by the Department of Educational Administra- 
tion of Teachers College, Columbia University. 

In the following summary the total improvement in silent reading dur- 
ing the three-year period from ages 10 to 13 inclusive is given for each 
of the school systems studied, and also the median ability for the re- 
spective groups of 13-year-old children. The schools are listed in the 
order of the amount of improvement made. 



58 Study of Achievement in Country and Town Schools 





Total gain 


Medians 


School Systems 


10 to 13 
inclusive 


13-year-old 
children 


Amsterdam. _ -- -- 


2.85 
1.90 
1.81 
1.58 
.76 


6 55 


Madison County, 9-month schools -. 


6 45 


Louisville . - -- 


6.90 


Hamilton Township.. .. . 


6.77 


Madison County, 6-month schools . . 


5.25 







The ranking in order of amount of improvement for the three-year 
period from ages 10 to 13 inclusive does not correspond exactly with 
the ranking in order of abihty of 13-year-old children. As has been 
pointed out in the case of language and arithmetic, the medians for 
13-year-old children may be affected by constant errors in any of the 
respective systems, such as a tendency to overrun the time allowance, 
a little greater leniency in scoring papers in one place than in another 
either by the teachers or by the examiner, in giving directions, etc. 
Such errors are compensating when the difference between the medians 
for two ages is used as a measure, since these errors would be constant 
for any given place and time for pupils of the diiTerent ages. In view 
of this, it is probable that the ranking in order of total gain in the above 
table is the more significant ranking. 

The amount of gain in the respective systems is directly comparable, 
since the scale used is expressed in terms of units of difficulty for the 
children. We can say that the results in Amsterdam for the three- 
year period from 10 to 13 inclusive are about four times as good as 
are the results in the Madison County 6-month schools, and about 
twice as good as the results in Hamilton Township. However, not 
all of the improvement noted is known to be the result of school pro- 
cedure. A good share of the gain in ability to read silently may be 
due to forces outside of the school, such as library facilities, home in- 
fluence, newspapers, etc. Indeed, it is sometimes charged that school 
work in reading stresses oral work too much.^ The conclusion from 
the above table is therefore limited to the statement that the sum of 
school influence in reading and outside influences in reading is about 
four times as great in Amsterdam as in the Madison County 6-month 
schools for the equal period of time from ages 10 to 13. If equality 
of outside influences making for improvement in silent reading might 
be assumed for the different systems studied, there would be left the 
single variable element in the school work on silent reading. It does 



^ For an example of this see Klapper, Teaching Children to Read. 



Achievement Measured by Thorndike Reading Scale 



59 



not seem probable, however, that influences other than those of the 
school which make for improvement in silent reading are equal in 
cases such as Amsterdam, New York, and the smaller schools of Mad- 
ison County, Kentucky. 

The following summary shows the gain for each age period of a 
year in the systems studied : 



School Systems 


Yearly Gains 




10 to 11 


11 to 12 


12 to 13 


Amsterdam.. . . __. 


1.67 
.75 
.94 

.72 
.03 


.62 
.56 
.42 
.34 
.59 


.56 


Madison County, 9- month schools 


.59 


Louisville.. . ._ ._ . _ . 


.45 


Hamilton Township . 


.52 


Madison County, 6-month schools . . 


.14 






Total 


4.11 


2.53 


2.26 







The variations in the amount of yearly gain are large, as is the case 
in language and arithmetic. The greatest gain seems to be from ages 
10 to 11, and each year after this shows less gain than the preceding 
year. It appears that greater gain is made by younger children than 
by older ones within the limits of the age-groups studied. 



CONCLUSIONS 

1. The difference in ability in silent reading, as measured by the 
Thorndike Silent Reading Scale Alpha 2, can be obtained for children 
of different ages. 

2. Since the function measured by this scale may be improved by 
influences outside of the school, as well as by school training, this dif- 
ference cannot be considered as a wholly reliable measure of school 
efficiency in teaching silent reading. 

3. This difference does give a reliable measure of the improvement 
in silent reading due to all causes during the three-year period from 
ages 10 to 13 inclusive. 

4. Since the improvement measured by this scale is stated in terms 
of difficulty for the children, the differences obtained in the respective 
systems studied may be compared directly. 

5. The differences obtained may be compared for two systems of 
schools, even though the testing was done at different times in the re- 
spective systems. 



60 Study of Achievement in Country and Town Schools 

6. The diflferences obtained are valid, even though there may be 
constant errors in the giving of the tests, such as might be caused by 
having the tests given by the teachers. 

7. Greater gain in silent reading seems to be made by the younger 
children within the age limits studied (ages 10 to 13 inclusive). 

8. Material gain in silent reading may be made during any part or all 
of the period from ages 10 to 13 inclusive. 

9. The results in the Madison County 6-month schools are much 
poorer than in any other system studied. 

10. The results in the Madison County 9-month schools compare 
favorably with those in the other systems studied. 



CHAPTER VI 
SUMMARY AND CONCLUSIONS 

This study was undertaken with four specific objects in mind. 
These objects are set forth in Chapter II, and are stated as follows : 

First : To show that the diflFerence in performance in school sub- 
jects of children of different ages can be obtained. 

Second: To show that this difference is a measure of school effi- 
ciency which may be used to measure schools or school systems. 

Third : To apply this measure to a system of country schools. 

Fourth : To compare the results in this country school system with 
the results in certain city school systems. 

The results of the study are considered in the light of these aims. 
Sections 1, 2, 3 and 4 of this chapter deal respectively with the pur- 
poses stated. 

Section 1 

The purpose as stated is "to show that the difference in perform- 
ance in school subjects of children of different ages can be obtained." 

With the tests used such differences have been obtained for chil- 
dren from 10 to 13 years of age inclusive. As the work progressed, 
certain difficulties became apparent which seem to justify the following 
statements : 

The tests to be used in obtaining age differences in performance 
must be of such a nature that identical tests can be given in identical 
manner to all of the grades tested. Such a spelling scale as that de- 
vised by Ayres could not give age differences because the 12-year-old 
child in the third grade would have a score on a test different from 
the test used for the 12-year-old child in the sixth grade. The results 
for children of like age, but in different grades, would be in terms that 
could not be directly compared. 

The tests should be given in as many as possible of the grades of 
the elementary school. The tabulations in this study include results 
for grades 3 to 8 inclusive and in some cases for grades 4 to 8. With 
results from children in these grades it was found necessary to esti- 
mate the number of children in the lower grades of the respective 
ages studied, and it seemed unwise to attempt to find medians for 

61 



62 Study of Achievement in Country and Tozvn Schools 

groups of children under 10 years of age because of the limited num- 
ber of children of the lower ages tested. If the tests could have been 
given in grade 2, it would have been possible to calculate medians for 
children under 10, and the necessity of calculating the probable num- 
ber of 10-to- 11 -year-old children in grade 2 would have been avoided, 
and scores could have been assigned them. 

Full age-grade tables of all the children in all the grades of the 
systems studied should be prepared. Such tables give a very desirable 
check on the number of children tested, and furnish a basis for esti- 
mation of the number of children of any given age in grades not tested. 

Tests used should be such as will test the ability of the children in 
the lower grades as well as the ability of those in the higher grades. 
The work with Courtis Standard Research Tests in Arithmetic showed 
that these tests do not measure the ability of lower grade children, 
since a great many children were unable to work correctly even one 
of the examples given. A test that includes problems less difficult than 
those of this series would be desirable. 

Tests used must be individual tests rather than group tests ; at least 
it must be possible to assign individual scores on the basis of the tests 
given. This is necessary in order that the individual scores of chil- 
dren of any given age may be taken from the different grades in which 
these children are tested and thrown into a single distribution on an 
age basis. 

For work in country schools there is an added need for individual 
tests rather than group tests, since groups of children of like age or 
grade in any given country school are likely to be small. 

The above statements may be summarized as a set of directions for 
the guidance of those giving tests which are to be tabulated on an age 
basis. The concise directions are as follows : 

1. Select tests that are identical for all the grades to be tested. 

2. Test as many of the grades as possible. 

3. Make full age-grade tables of all the children in all the grades. 

4. Select tests that measure the ability of all the children. 

5. Use individual rather than group tests. 

Section 2 

The second purpose of this study as stated is "to show that this dif- 
ference is a measure of school efficiency which may be used to meas- 
ure schools or school systems." 

In so far as the tests used measure functions affected solely, or even 



Summary and Conclusions 63 

largely, by school training, the difference in performance of children 
of different ages seems to furnish a measure of school efficiency. In 
the case of the Trabue Language Scale B the function measured has 
not been shown to be fundamentally one dependent on school training. 
In the case of the Courtis Standard Research Tests in Arithmetic 
Series B it seems that the function measured is to a very large degree 
at least one dependent on school training ; therefore in this case the 
difference obtained is one that is chiefly the direct result of the school 
training received by the children and of elimination, and for that rea- 
son may be considered a measure of the effectiveness of that training 
and of elimination. In the case of the Thorndike Silent Reading Scale 
Alpha 2 the function measured is one which is greatly affected by 
school training, but which may also be greatly affected by influences 
outside of the school. 

Even though the function measured be one which is affected by in- 
fluences other than school training, it may be argued that the work 
of the school should so supplement other influences brought to bear 
upon the children as to secure for them reasonable development of 
the function considered. If this conception of the work of the school 
is accepted, the difference between performance of children of differ- 
ent ages seems a sound measure of the degree to which the school has 
succeeded in its effort to secure the desired development. 

In any case in which the difference in performance of children of 
different ages is considered as measuring some function other than 
one dependent on school training for its improvement, the difficulty 
lies in the nature of the test rather than in the fact that the age-differ- 
ences are used. The same criticism would apply to the same meas- 
urement if grade standards were used. 

There are a few advantages that the use of age-differences as a 
measure of school efficiency seems to have over the use of grade 
standards. One of these is that the testing may be done at any con- 
venient time in the school year, with the possible exception of the first 
three or four weeks of the school term. This is due to the fact that 
the birthdays of any age-group of children, say the 10-year-olds, are 
distributed throughout the year in the same way as are the birthdays 
of any other age-group, say the 13-year-olds. This means that the loss 
of children from the group because they reach a higher age will be 
compensated by the accretion of other children from the next lower 
age-group. Moreover, this loss and accretion continues throughout 
the school year and for each age-group, so that the difference between 



64 Study of Achievement in Country and Town Schools 

any two age-groups is a constant quantity. During the first few weeks 
of school there may be a shghtly uneven loss in school ability due to 
the vacation period, since it has never been shown that the retaining 
power of children of different ages is the same. After school is once 
well under way this uneven loss is overcome, and the testing may be 
done at any convenient time. 

Another advantage in the use of age-diflferences as a measure 
of school efficiency lies in the fact that errors such as those caused by 
having the tests given by the teachers are compensated, since such er- 
rors are identical for children of all ages. 

A further advantage in the use of age-differences lies in the fact 
that the effects of poor grading or great retardation are considered in 
the measurement of improvement. The necessity of correcting grade 
results for retardation is avoided, since the score of the retarded child 
of any given age has entered into the measurement of that age-group. 

The advantages mentioned above are of particular significance for 
work in country schools. The difficulties involved in giving tests 
where the schools are scattered, the grading poor, and the groups of 
children frequently very small, make it especially desirable to give 
tests in these schools at the most convenient time of the year and to 
have the tests given by the teacher. 

Section 3 

The third purpose of this study as stated is "to apply this measure 
to a system of country schools." 

This purpose has been accomplished and the results given in the 
treatment of the respective tests. 

Section 4 

The fourth purpose of this study as stated is "to compare the re- 
sults in this country school system with the results in certain city 
school systems." 

The Madison County 6-month schools have been compared through- 
out this study with the schools in the same county having a 9-month 
school term. In addition to this comparison, the results of the Trabue 
Language Scale B have been compared with results from Louisville, 
Kentucky ; Paterson, New Jersey ; and St. Paul, Minnesota. As has 
already been pointed out, this comparison concerns the results of 
school training and also other influences. The 9-month schools in 
Madison County made a gain in the ability to complete sentences 53 



Summary and Conclusions 65 

per cent greater than the gain made over the same three-year period 
in the 6-month schools. None of the systems studied made a gain so 
great as that of the Madison County 9-month schools, and all of them 
except St. Paul made gains greater than did the Madison County 
6-month schools. St. Paul made practically the same gain as did these 
schools. 

If the comparison is made on the basis of the final ability attained 
by the children (medians for 13-year-olds), the Madison County 6- 
month schools are poorer than any of the others studied. Louisville 
13-year-old children possess 50 per cent greater ability to complete 
sentences than do those in the smaller schools of Madison County. 
The children of the same age in the 9-month schools possess 25 per 
cent greater ability than do the children of the 6-month schools. The 
10-year-old children in Louisville possess greater ability to complete 
sentences than do the 13-year-old children in the 6-month Madison 
County schools, and so do the 12-year-old children in the 9-month 
schools, the 11-year-olds in Paterson and the 10-year-olds in St. Paul. 

Whichever basis of comparison is used, the Madison County 6- 
month schools are at the bottom. If the age achievement is used 
as the basis of comparison, the Madison County 9-month schools are 
only kept from the bottom by the presence of the 6-month schools 
among the systems compared. 

In comparing the work in arithmetic it must be remembered that 
the results are in terms of examples worked correctly in a given length 
of time, and that it cannot be assumed that it is twice as difficult to 
add 8 examples as it is to add 4 in the same time. Bearing in mind 
this caution, it seems, on the basis of the results obtained, that while 
the pupil in the Madison County 6-month schools is increasing his 
ability to add to such an extent that he can add one more example in 
the time allowed, the pupil in the Madison County 9-month schools is 
increasing his ability to add by 1.6 examples, the pupil in Louisiana by 
2.2, the one in Arkansas City by 2.7, the one in Salina by 3.0, the one in 
Louisville by 3.4, and the one in Hibbing by 5.7 examples. 

In subtraction the situation is much the same. While the pupil in 
the Madison County 6-month schools is improving his ability to sub- 
tract by 1 example, the one in the 9-month schools of the same county 
is improving his ability by 3.1, the one in Salina by 3.2, the one in 
Louisiana by 3.3, the one in Arkansas City by 4.2, the one in Louis- 
ville by 4.8, and the one in Hibbing by 5.8 examples. 



66 Study of Achievement in Country and Town Schools 

While, the pupil in the 6-month schools of Madison County is im- 
proving his ability to multiply to such an extent that he can multiply 
one more example in the time allowed, the pupil in Louisiana improves 
his ability so that he can multiply 5.8 more examples in the time al- 
lowed, the pupil in the Madison County 9-month schools improves by 
6.2 examples, the one in Louisville by 7.7, the one in Salina by 7.8, 
the one in Arkansas City by 8.8, and the one in Hibbing by 12.5 ex- 
amples. 

In division the situation is even worse. While an improvement of 
one example is being made by the pupil in the Madison County 6- 
month schools, there is an improvement of 6.1 by the pupil in the 
Louisiana schools, of 6.8 in the Madison County 9-month schools, of 
9.1 in Arkansas City, of 13.4 in Salina, of 16.1 in Louisville, and of 
23.4 in Hibbing. 

If the comparison be put on the basis of achievement of 13-year-old 
children, the situation in the Madison County 6-month schools does 
not seem to be much better. The median 13-year-old child in these 
schools can neither add, subtract, nor multiply as well as the median 
10-year-old in Hibbing, and he can barely divide as well. The Madi- 
son County 9-month schools do better on this basis, but the median for 
the 13-year-old children is below the median for the 11-year-old chil- 
dren in Hibbing in addition, subtraction, multiplication and division. 

The comparison of the results of the Thorndike Silent Reading 
Tests shows conditions which are not quite so disastrous for the 
Madison County 6-month schools in that the differences are not so 
great. On the basis of improvement, while the pupil in the Madison 
County 6-month schools is improving his ability to read by one step 
on the Thorndike scale, the pupil in Hamilton Township improves 2.1 
steps, the one in Louisville 2.4, in the Madison County 9-month schools 
2.5, and in Amsterdam Z.7 steps. On the basis of age achievement 
the median 13-year-old child in the Madison County 6-month schools 
is poorer than the median 11 -year-old child in Hamilton Township, 
Louisville, and Amsterdam, and almost as poor as the median 11 -year- 
old child in the Madison County 9-month schools. 

The comparison of the Madison County 6-month schools with the 
other schools tested may be summed up in the statement that the chil- 
dren in these schools have less ability along every line tested than have 
the children of the same ages in other schools, and that they are learn- 
ing more slowly, except that the children in St. Paul are improving as 
slowly as they do in language. 



Summary and Conclusions 67 

Final Summary 

The following four statements seem justified concerning the four 
purposes for which this study was undertaken : 

First: The difference in performance in school subjects can be ob- 
tained for children of different ages. 

Second: This difference is a measure which may be used to meas- 
ure schools or school systems, and has certain advantages for this pur- 
pose, especially in rural schools. 

Third : This measure has been applied to a system of country 
schools. 

Fourth : The Madison County 6-month schools compare unfavor- 
ably with all of the other schools measured. The Madison County 
9-month schools compare more favorably. 



APPENDIX 



For the convenience of any who may wish to supplement the re- 
port made in Chapter I of scientific studies on the results of instruc- 
tion in rural schools, or who may later wish to bring this report up to 
date, this statement of the educational literature investigated is made. 

As a first step in searching for such data the following surveys were 
studied. In each case the tables showing the results were investigated 
to find what scores might be included from rural schools in the com- 
parisons made. 

SURVEYS 



Akron, Ohio. 

Alabama (three counties). 

Alabama.* 

Alton, 111. 

Amsterdam, N. Y. 

Anderson, Ind. 

Arizona.* 

Ashland, Ore. 

Atlanta, Ga. 

Baltimore, Md. 

Binghamton, N. Y. 

Blaine, Wash. 

Bloommgton, Ind. 

Boise, Idaho. 

Boston, Mass. 

Bridgeport, Conn. 

Buffalo, N. Y. 

Brookline, Mass. 

Butte, Mont. 

Chicago, 111. (Educational Commission). 

Cincinnati, Ohio. 

Cleveland, Ohio. 

Cleveland, Ohio.f 

Colorado. 

Cold Springs, N. Y. (Haldane School). 

Colorado (rural schools). 

Columbia, S. C. 

Connecticut (Educational Commission). 



Connecticut (counties). 

Dansville, N. Y. (High School). 

Dayton, Ohio. 

Delaware.J 

Delaware (School Buildings). 

Denver, Col. 

Detroit, Mich. (Recreational). 

Elyria, Ohio.* 

Evansville, Ind. (Vocational). 

Framingham, Mass. 

Gary, Ind.* 

Gary, Ind. J 

Georgia (Counties). 

Grafton, W. Va. 

Grand Junction, Col. 

Grand Rapids, Mich. 

Great Neck, L. I. 

Greene County, Ind. 

Greenwich, Conn. 

Hammond, Ind. (Industrial). 

Harrisburg, Pa. 

Herkimer, N. Y. 

Huron County. 

Illinois (State). 

Indiana (Vocational). 

Janesville, Wis. 

Jefferson County, Ind. (Vocational). 

Kansas (high schools). 



*United States Bureau of Education. 
tRussell Sage Foundation. 
JGeneral Education Board. 



68 



Appendix 



69 



Lane County, Ore. 

Los Angeles, Cal. 

Leavenworth, Kan. 

Louisville, Ky. 

Maricopa County, Ga. 

Maryland (State). J 

Memphis, Tenn.* 

Minneapolis, Minn. (Vocational). 

Missouri (Saline County). 

Montclair, N. J. 

Nassau County, N. Y. 

Newburgh, N. Y. 

New Orleans, La. (Vocational). 

Newton, Mass. 

New York City. 

North Dakota.* 

Oakland, Cal. 

Ogden, Utah. 

Ohio. 

Oklahoma. 

Oklahoma (county). 

Oswego County, N. Y. 

Paducah, Ky. 

Paterson, N. J. 

Port Townsend, Wash. 

Portland, Ore. 

Reading, Pa. 



Rochester, Minn. 

Rockford, 111. 

St. Louis, Mo. 

St. Paul, Minn. 

Salt Lake City, Utah. 

San Antonio, Texas. 

San Francisco, Cal. 

San Mateo, Cal. 

Saskatchewan, Canada. 

Solvay, N. Y. 

South Bend, Ind. 

South Dakota.* 

Stamford, Conn. 

Syracuse, N. Y. 

Travis County, Texas. 

Utica, N. Y. 

Van Wert, Ohio. 

Vermont.f 

Virginia (Educational Commission). 

Washington.* 

Waterbury, Conn. 

Westchester, N. Y. 

Wilmington, Del.* 

Windsor County, Vt. 

Wisconsin (State). 

Winston-Salem, N. C. 

Wyoming.* 



The next step in the search for data bearing on the objective results 
of instruction in rural schools was a study of A Selected Bibliography 
of Certain Phases of Educational Measurements, prepared by Edna 
Bryner and published in the Seventeenth Year Book of the National 
Society for the Study of Education, 1918. The titles listed were 
exainined, and whenever there seemed any possibility that the article 
might contain any data concerning country schools the article was stud- 
ied. One bulletin by E. J. Ashbaugh, entitled The Arithmetical Skill 
of Iowa School Children, University of Iowa Extension Bulletin, No. 
24, November, 1916, was not found. In all, twenty-eight of the ref- 
erences were examined, and of these five were found to contain data. 

As a final step in the search for material bearing on the comparison 
of country and city schools by the use of objective standards, a study 
was made of the monthly lists of current educational publications pre- 



*United States Bureau of Education. 
fRussell Sage Foundation. 
JGeneral Education Board. 



70 Study of Achievement in Country and Town Schools 

pared by the United States Bureau of Education, beginning with the 
list for June, 1917, and extending through the list for October, 1920. 
In this study every title and subtitle was considered, and in case 
there seemed a possibility that objective data might be found, the 
reference was investigated. In this study only two articles which 
seemed to bear in any way on this topic were not found. These refer- 
ences are: (1) Johnson, W. E., "Reading, Writing, Arithmetic and 
Spelling in City and Town Schools of South Dakota in 1917-1918," 
Bulletin of the Northern Normal and Industrial School at Aberdeen, 
S. D., Vol. XII, No. 2 (October, 1918) ; and (2) Heckert, J. W., 
"The Cleveland Survey Tests in Arithmetic in the Miami Valley," 
Elementary School Journal, XVIII : 447-457. 









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